8. Rational Expressions and Functions

Find the least common denominators of the rational expressions:

$\frac{2x^2+5x-3}{x^2-9},\frac{4x-12}{x^2-x-6},\frac{x^2+x-2}{x^2-4x+3}$

Rewrite the expression $\frac{2x^2+2x}{-x^2+1}$ into an equivalent expression having a denominator of $x-1$.

Find the least common denominators of the rational expressions:

$\frac{2y^2+3y-5}{y^2-4}$, $\frac{y-2}{y^2+y-6}$

Rewrite the expression $\frac{3}{x+2}$ into an equivalent expression having a denominator of $(x+2)(x+5)$.

Find the least common denominators of the rational expressions:

$\frac{3x^2-12}{x^2-x-6}$, $\frac{5x+10}{x^2-4x+3}$

Rewrite the expression $\frac{7x^2+7x}{x^2-1}$ into an equivalent expression having a denominator of $x-1$.