Divide each expression and write the quotient in its simplest form. 5 p + 5 8 − 10 p ÷ 3 p + 3 2 ( 8 − 10 p ) \frac{5p+5}{8-10p}\div\frac{3p+3}{2(8-10p)}

This problem asks us to divide each expression and write the quotient in its simplest form. So we have five p plus five over eight minus 10 p divided by three p plus three over two times eight minus 10 p. So let's see how we can go about dealing with this. Well, remember the rule when it comes to dividing rational expressions. We can use keep, change, flip. So I'm gonna keep the five p plus five over eight minus 10 p. I'm going to change the division to multiplication, and then I'm going to flip the second fraction. So we'll have two times eight minus 10 p, and then all of that's going to be over three p plus three. Now what can I do from here? Well, this is a point where we want to focus on simplifying and factoring. So what I'm going to do is multiply straight across, and as I go through this step, I'm going to simplify what I can. Now one thing that I see is I have a five in common right about here. So I'm gonna pull that five out to the front, and then we're going to have p plus one, just dividing out five from each of these terms. Now it's going to be multiplied by two times eight minuteus 10 p. We've gone ahead and multiplied across, and we've reverse distributed this five. Now let's move to the denominator. Well, in the denominator I have eight minuteus 10 p, and that's being multiplied by three p plus three, which I can go ahead and pull out a three from each of these terms giving me times three times p plus one. Now after pulling everything out, notice what happens here, the p plus one in the numerator and denominator will cancel. The eight minus 10 p will cancel as well. So all we end up with in the numerator is five times two, which is 10, and all we end up in the denominator is three. So 10 over three is the simplified final answer to this expression when we divide, and that's how you can solve these types of problems.

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1. Review of Real Numbers2h 43m

Simplifying Fractions
30m

Evaluating Exponents
29m

Evaluating Expressions
15m

Translating Phrases to Expressions
16m

Translating Sentences to Equations
9m

The Distributive Property
17m

Simplifying Expressions
44m

2. Linear Equations and Inequalities5h 35m

Solving Linear Equations
2h 23m

Linear Inequalities in One Variable
46m

Set Operations and Compound Inequalities
1h 7m

Absolute Value Equations
38m

Absolute Value Inequalities
39m

3. Solving Word Problems2h 46m

Introduction to Problem Solving
37m

Formulas
25m

Percent Problem Solving
59m

Mixture Problem Solving
43m

4. Graphs and Functions5h 12m

The Rectangular Coordinate System
44m

Graph Linear Equations in Two Variables
24m

Graph Linear Equations Using Intercepts
23m

Slope of a Line
44m

Slope-Intercept Form
38m

Point Slope Form
22m

Linear Inequalities in Two Variables
28m

Introduction to Relations and Functions
53m

Function Notation
15m

Composition of Functions
17m

5. Systems of Linear Equations1h 53m

Solving Systems of Linear Equations by Graphing
29m

Solving Systems of Linear Equations by Substitution
15m

Solving Systems of Linear Equations by Elimination
45m

Systems of Linear Inequalities
23m

6. Exponents, Polynomials, and Polynomial Functions3h 17m

The Product Rule
9m

The Quotient Rule
10m

Intro to the Power Rules
17m

The Power of a Quotient Rule
13m

Negative Exponents
24m

Simplifying Exponential Expressions Using All Exponent Rules
6m

Intro to Polynomials
21m

Adding and Subtracting Polynomials
20m

Multiplying Polynomials
38m

Special Products
34m

7. Factoring2h 49m

Factoring by Greatest Common Factor & Grouping
37m

Factoring Trinomials of the Form x² + bx + c
11m

Factoring Trinomials of the Form ax² + bx + c
37m

Factoring Special Products
41m

Quadratic Equations & Applications
41m

8. Rational Expressions and Functions3h 44m

Simplifying Rational Expressions
42m

Multiplying and Dividing Rational Expressions
25m

Adding and Subtracting Rational Expressions with Common Denominators
19m

Least Common Denominators
32m

Adding and Subtracting Rational Expressions with Different Denominators
32m

Rational Equations
44m

Direct & Inverse Variation
27m

9. Roots, Radicals, and Complex Numbers3h 57m

Introduction to Radical Expressions
47m

Simplifying Radical Expressions
47m

Adding and Subtracting Radicals
19m

Multiplying, Dividing, and Rationalizing Radicals
53m

Introduction to Complex Numbers
18m

Multiplying and Dividing Complex Numbers
51m

10. Quadratic Equations and Functions3h 1m

The Square Root Property
25m

Completing the Square
26m

The Quadratic Formula
40m

Graphing Quadratic Equations
1h 28m

11. Inverse, Exponential, & Logarithmic Functions2h 30m

Introduction to Inverse Functions
25m

Exponential Functions
35m

Introduction to Logarithmic Functions
33m

Properties of Logarithms
54m

12. Conic Sections & Systems of Nonlinear Equations2h 24m

Graphing Circles
32m

Ellipses
35m

Parabolas
35m

Hyperbolas
41m

13. Sequences, Series, and the Binomial Theorem1h 51m

Introduction to Sequences
40m

Arithmetic Sequences
27m

Geometric Sequences
29m

Factorials
13m

8. Rational Expressions and Functions

Multiplying and Dividing Rational Expressions

Intermediate Algebra

8. Rational Expressions and Functions

Multiplying and Dividing Rational Expressions

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Multiple Choice

Divide each expression and write the quotient in its simplest form.
$\frac{5 p + 5}{8 - 10 p} \div \frac{3 p + 3}{2 (8 - 10 p)}$

$\frac{10}{3}$

$\frac{3}{10}$

$$\frac$53$

$$\frac$13$

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Verified step by step guidance

Rewrite the division of fractions as multiplication by the reciprocal. The expression is: $\frac{5p+5}{8-10p} \div \frac{3p+3}{2(8-10p)}$. This becomes $\frac{5p+5}{8-10p} \times \frac{2(8-10p)}{3p+3}$.

Factor common terms in the numerators and denominators where possible. For example, factor $5p+5$ as $5(p+1)$ and $3p+3$ as $3(p+1)$.

Substitute the factored forms back into the expression: $\frac{5(p+1)}{8-10p} \times \frac{2(8-10p)}{3(p+1)}$.

Cancel out common factors that appear in both numerator and denominator, such as $(p+1)$ and $(8-10p)$, to simplify the expression.

Multiply the remaining factors in the numerator and denominator to write the quotient in simplest form.

2:44m

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Divide each expression and write the quotient in its simplest form.5p+58−10p÷3p+32(8−10p)\(\frac{5p+5}{8-10p}\[\div\]\frac{3p+3}{2(8-10p)}\)

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Divide each expression and write the quotient in its simplest form.
$\frac{5 p + 5}{8 - 10 p} \div \frac{3 p + 3}{2 (8 - 10 p)}$