Answer:
(x-3)
Step-by-step explanation:
we have
[tex]\frac{x^{2}+7x-30}{x+10}[/tex]
step 1
Simplify the numerator
Complete the square
Equate the equation to zero
[tex]x^{2}+7x-30=0[/tex]
[tex]x^{2}+7x=30[/tex]
[tex]x^{2}+7x+3.5^{2}=30+3.5^{2}[/tex]
[tex]x^{2}+7x+12.25=42.25[/tex]
Rewrite as perfect squares
[tex](x+3.5)^{2}=42.25[/tex]
Take square root both sides
[tex](x+3.5)=(+/-)6.5[/tex]
[tex]x=-3.5(+/-)6.5[/tex]
[tex]x=-3.5(+)6.5=3[/tex]
[tex]x=-3.5(-)6.5=-10[/tex]
therefore
[tex]x^{2}+7x-30=(x-3)(x+10)[/tex]
substitute in the numerator
[tex]\frac{x^{2}+7x-30}{x+10}=\frac{(x-3)(x+10)}{x+10}=x-3[/tex]
