How do you simplify $\frac{x^{2} - 9}{x + 2} \div \frac{x^{2} + x - 6}{x^{2} - 4}$ $(x^2-9)/(x+2)div(x^2+x-6)/(x^2-4)$ ?

Question

How do you simplify $\frac{x^{2} - 9}{x + 2} \div \frac{x^{2} + x - 6}{x^{2} - 4}$ $(x^2-9)/(x+2)div(x^2+x-6)/(x^2-4)$ ?

1 Answer

Impact of this question

3070 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-05-02T23:16:09

Invert the divisor polynomial, then multiply (factor) and simplify.
$\frac{\frac{a}{b}}{\frac{c}{d}} = (\frac{a}{b}) \cdot (\frac{d}{c}) = \frac{a \cdot d}{b \cdot c}$ $(a/b)/(c/d) = (a/b) * (d/c) = (a*d) / (b*c)$

Explanation:

$\frac{x^{2} - 9}{x + 2} \div \frac{x^{2} + x - 6}{x^{2} - 4} =$ $(x^2-9)/(x+2)div(x^2+x-6)/(x^2-4)=$ ,invert the divisor and multiply

$\frac{x^{2} - 9}{x + 2} \cdot \frac{x^{2} - 4}{x^{2} + x - 6} =$ $(x^2-9)/(x+2)*(x^2-4)/(x^2+x-6)=$

$\frac{(x^{2} - 9) \cdot (x^{2} - 4)}{(x + 2) \cdot (x^{2} + x - 6)} =$ $((x^2-9) * (x^2-4)) / ((x+2)*(x^2+x-6))=$ ,then factor and reduce

$\frac{(x + 3) (x - 3) (x + 2) (x - 2)}{(x + 2) (x + 3) (x - 2)} =$ $((x+3)(x-3)(x+2)(x-2)) / ((x+2)(x+3)(x-2))=$

$((cancel(x+3)) (x-3) (cancel(x+2)) (cancel(x-2))) / (cancel((x+2))cancel((x+3)) cancel((x-2)))=$

$x-3$

Science

Math

Humanities

... and beyond

How do you simplify $\frac{x^{2} - 9}{x + 2} \div \frac{x^{2} + x - 6}{x^{2} - 4}$ $(x^2-9)/(x+2)div(x^2+x-6)/(x^2-4)$ ?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you simplify (x^2-9)/(x+2)div(x^2+x-6)/(x^2-4)x2−9x+2÷x2+x−6x2−4(x^2-9)/(x+2)div(x^2+x-6)/(x^2-4)?

1 Answer

Explanation:

Related questions

Impact of this question

How do you simplify $\frac{x^{2} - 9}{x + 2} \div \frac{x^{2} + x - 6}{x^{2} - 4}$ $(x^2-9)/(x+2)div(x^2+x-6)/(x^2-4)$ ?