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

Question

asked Apr 16, 2023 37.9k views

1 Answer

Nisan · Answer 1 · 2023-04-21T14:32:02+0000

Answer:
$\begin{gathered} Simplest\text{ form: }(x+2)/(x-7) \\ \\ Restriction:\text{ x ^^^^2260 7} \end{gathered}$ Step-by-step explanation:

The given expression is:

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:

The restriction is:

x ≠ 7