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Evaluate the expression for $x = -3$ . $\newline$ Write your answer in simplest form. $\newline$ $\frac{x - 6}{x - 3} = \underline{\hspace{2em}}$

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Evaluate rational expressions II

Full solution

Q. Evaluate the expression for

x = -3

.

\newline

Write your answer in simplest form.

\newline

\frac{x - 6}{x - 3} = \underline{\hspace{2em}}

Identify Expression: Identify the expression after substituting $x = -3$ $\newline$ Substitute $-3$ for $x$ in $\frac{x - 6}{x - 3}$ . $\newline$ $\frac{(-3) - 6}{(-3) - 3}$
Substitute and Simplify: Evaluate $(-3) - 6$ $(-3) - 6 = -9$ Numerator: $-9$
Evaluate Numerator: Evaluate $-3 - 3$ $-3 - 3 = -6$ 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 $3$ . $\newline$ $= \frac{3}{2}$

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