Skip to main content
Ch. P - Fundamental Concepts of Algebra
Blitzer - College Algebra 8th Edition
Blitzer8th EditionCollege AlgebraISBN: 9780136970514Not the one you use?Change textbook
All textbooksBlitzer 8th EditionCh. P - Fundamental Concepts of AlgebraProblem 117
Chapter 1, Problem 117

Add or subtract as indicated. 12/25x^2+11/15x^3

Verified step by step guidance
1
Step 1: Identify the terms in the expression. The given expression is \( \frac{12}{25}x^2 + \frac{11}{15}x^3 \). Notice that the terms have different powers of \(x\), so they are not like terms and cannot be directly added or subtracted.
Step 2: Factor out the greatest common factor (GCF) if possible. In this case, the coefficients \( \frac{12}{25} \) and \( \frac{11}{15} \) do not share a common factor, and the powers of \(x\) are different, so no factoring is possible.
Step 3: Rewrite the expression as it is already simplified. Since the terms are not like terms, the expression remains \( \frac{12}{25}x^2 + \frac{11}{15}x^3 \).
Step 4: If required, you can express the terms with a common denominator for the coefficients. The least common denominator (LCD) of \(25\) and \(15\) is \(75\). Rewrite each fraction with a denominator of \(75\): \( \frac{12}{25} = \frac{36}{75} \) and \( \frac{11}{15} = \frac{55}{75} \). The expression becomes \( \frac{36}{75}x^2 + \frac{55}{75}x^3 \).
Step 5: Combine the rewritten terms if necessary. Since the terms still have different powers of \(x\), they cannot be combined further. The final simplified expression is \( \frac{36}{75}x^2 + \frac{55}{75}x^3 \).

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
3m
Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Rational Expressions

Rational expressions are fractions where the numerator and the denominator are polynomials. To add or subtract these expressions, it is essential to have a common denominator. This involves finding the least common multiple (LCM) of the denominators, which allows for the combination of the fractions into a single expression.
Recommended video:
Guided course
02:58
Rationalizing Denominators

Finding a Common Denominator

Finding a common denominator is a crucial step in adding or subtracting rational expressions. The common denominator must be the least common multiple of the individual denominators. Once identified, each fraction is adjusted by multiplying its numerator and denominator by the necessary factors to achieve this common denominator, enabling the fractions to be combined.
Recommended video:
Guided course
02:58
Rationalizing Denominators

Combining Like Terms

Combining like terms involves simplifying expressions by adding or subtracting coefficients of terms that have the same variable raised to the same power. After obtaining a common denominator and combining the numerators, it is important to simplify the resulting expression by merging any like terms, which streamlines the final answer and makes it easier to interpret.
Recommended video:
5:22
Combinations
Related Practice
Textbook Question

In Exercises 121–128, write each English phrase as an algebraic expression. Then simplify the expression. Let x represent the number. A number decreased by the sum of the number and four

Textbook Question

Simplify each complex rational expression. (1/x-1/2)/(1/3-x/6)

Textbook Question

In Exercises 111–120, use the order of operations to simplify each expression. 6(−4)−5(−3)/(9−10)

1
views
Textbook Question

Add or subtract as indicated. [(2x-7)/(x^2-9)]-[(x-10)/(x^2-9)]

Textbook Question

In Exercises 107–114, simplify each exponential expression. Assume that variables represent nonzero real numbers. (2^−1x^−3y^−1)^−2(2x^−6y^4)^−2(9x^3y^−3)^0/(2x^−4y^−6)^2

2
views
Textbook Question

In Exercises 111–120, use the order of operations to simplify each expression. 8−3[−2(2−5)−4(8−6)]

1
views