Question

Simplify completely x^2+7x-30/x+10

Answer 1

Answer:

(x-3)

Step-by-step explanation:

we have

$\frac{x^{2}+7x-30}{x+10}$

step 1

Simplify the numerator

Complete the square

Equate the equation to zero

$x^{2}+7x-30=0$

$x^{2}+7x=30$

$x^{2}+7x+3.5^{2}=30+3.5^{2}$

$x^{2}+7x+12.25=42.25$

Rewrite as perfect squares

$(x+3.5)^{2}=42.25$

Take square root both sides

$(x+3.5)=(+/-)6.5$

$x=-3.5(+/-)6.5$

$x=-3.5(+)6.5=3$

$x=-3.5(-)6.5=-10$

therefore

$x^{2}+7x-30=(x-3)(x+10)$

substitute in the numerator

$\frac{x^{2}+7x-30}{x+10}=\frac{(x-3)(x+10)}{x+10}=x-3$