"Perform the multiplication or division and simplify. x+34x2−9÷x2+7x+1222+7x−15" was answered by our community

High School
Algebra
Algebra I
Quadratic function and equation

Miracle Graves

Answered question

2022-02-15

Perform the multiplication or division and simplify.

\frac{x + 3}{4 x^{2} - 9} \div \frac{x^{2} + 7 x + 12}{2^{2} + 7 x - 15}

Answer & Explanation

rossegues03b

Beginner2022-02-16Added 11 answers

simplify:
$\frac{x + 3}{4 x^{2} - 9} \div \frac{x^{2} + 7 x + 12}{2^{2} + 7 x - 15}$
Inverting and changing to multiplication:
$\frac{x + 3}{4 x^{2} - 9} \div \frac{x^{2} + 7 x + 12}{2^{2} + 7 x - 15}$
$= \frac{x + 3}{4 x^{2} - 9} \times \frac{x^{2} + 7 x + 12}{2^{2} + 7 x - 15}$
factorizing the quadratics:
$= \frac{x + 3}{{(2 x)}^{2} - 3^{2}} \times \frac{2 x^{2} + 10 x - 15}{x^{2} + 4 x + 12}$
$= \frac{x + 3}{(2 x - 3) {(2 x + 3)}^{{}} \times \frac{2 x (x + 5) - 3 (x + 5)}{x (x^{+} 4) + 3 (x + 4)}$
$= \frac{x + 3}{(2 x - 3) {(2 x + 3)}^{{}} \times \frac{(2 x - 3) (x + 5)}{(x + 3) (x + 4)}$
cancelling the same terms, we get:
$= \frac{⧸ x + 3}{⧸ 2 x - 3 {(2 x + 3)}^{{}} \times \frac{⧸ 2 x - 3 (x + 5)}{⧸ x + 3 (x + 4)}$
$= \frac{(x + 5)}{(2 x + 3) {(x + 4)}^{{}}$

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