Simplify (x^2+4x-21)/(x^2+x-42)

$\frac{x^{2} + 4 x - 21}{x^{2} + x - 42}$

Step 1

Factor $x^{2} + 4 x - 21$ using the AC method.

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 21$ and whose sum is $4$ .

$- 3, 7$

Write the factored form using these integers.

$\frac{(x - 3) (x + 7)}{x^{2} + x - 42}$

Step 2

Factor $x^{2} + x - 42$ using the AC method.

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 42$ and whose sum is $1$ .

$- 6, 7$

Write the factored form using these integers.

$\frac{(x - 3) (x + 7)}{(x - 6) (x + 7)}$

Step 3

Cancel the common factor of $x + 7$ .

Cancel the common factor.

$\frac{(x - 3) (x + 7)}{(x - 6) (x + 7)}$

Rewrite the expression.

$\frac{x - 3}{x - 6}$

Simplify (x^2+4x-21)/(x^2+x-42)

Related Questions

Support LCMGCF.com by disabling your adblocker.