Question

What is x^2 + 4x + 4 ——————— x^2 - 5x -14 in simplest form? State any restrictions on the variable. The simplest form is _______.

Answer 1

Answer:
Step-by-step explanation:

The given expression is:

`(x^2+4x+4)/(x^2-5x-14)`

Factorize the numerator

`\begin{gathered} x^2+4x+4 \\ \\ x^2+2x+2x+4 \\ \\ x(x+2)+2(x+2) \\ \\ (x+2)(x+2) \end{gathered}`

Factorize the denominator

`\begin{gathered} x^2-5x-14 \\ \\ x^2-7x+2x-14 \\ \\ x(x-7)+2(x-7) \\ \\ (x+2)(x-7) \end{gathered}`

The given quotient expression then becomes:

`\begin{gathered} ((x+2)(x+2))/((x+2)(x-7)) \\ \\ (x+2)/(x-7) \end{gathered}`

The simplest form is:

`(x+2)/(x-7)`

The restriction is:

x ≠ 7