Evaluate the expression for x = -2. Write your answer in simplest form. x - 7/-x - 8 = ____

Identify Expression: Identify the expression after substituting x = -2 Substitute -2 for x in (x - 7)/(-x - 8). ((-2) - 7)/(-(-2) - 8)Substitute x = -2: Evaluate (-2) - 7 (-2) - 7 = -9 Numerator: -9Evaluate Numerator: Evaluate -(-2) - 8 -(-2) - 8 = 2 - 8 = -6 Denominator: -6Evaluate Denominator: -9/(-6) Rewrite the fraction in simplest form. Divide both -9 and -6 by their greatest common divisor, which is 3. (-9)/(-6) = (3 * -3)/(3 * -2) Cancel out the negative signs and the common factor of 3. = 3/2

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Evaluate the expression for $x = -2$ . $\newline$ Write your answer in simplest form. $\newline$ $\frac{x - 7}{-x - 8} = \underline{\hspace{2em}}$

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Algebra 2

Evaluate rational expressions II

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Q. Evaluate the expression for

x = -2

\newline

Write your answer in simplest form.

\newline

\frac{x - 7}{-x - 8} = \underline{\hspace{2em}}

Identify Expression: Identify the expression after substituting $x = -2$ $\newline$ Substitute $-2$ for $x$ in $\frac{x - 7}{-x - 8}$ . $\newline$ $\frac{(-2) - 7}{-(-2) - 8}$
Substitute $x = -2$ : Evaluate $(-2) - 7$ $\newline$ $(-2) - 7 = -9$ $\newline$ Numerator: $-9$
Evaluate Numerator: Evaluate $-(-2) - 8$ $-(-2) - 8 = 2 - 8 = -6$ Denominator: $-6$
Evaluate Denominator: $-\frac{9}{-6}$ $\newline$ Rewrite the fraction in simplest form. $\newline$ Divide both $-9$ and $-6$ by their greatest common divisor, which is $3$ . $\newline$ $\frac{-9}{-6} = \frac{3 \times -3}{3 \times -2}$ $\newline$ Cancel out the negative signs and the common factor of $3$ . $\newline$ $= \frac{3}{2}$