Multiply.
$$
\frac{x+3}{x^{2}-5 x+6} \cdot \frac{4 x-12}{x+2}
$$

Simplify your answer as much as possible.

Question

Multiply.
$$
\frac{x+3}{x^{2}-5 x+6} \cdot \frac{4 x-12}{x+2}
$$

Simplify your answer as much as possible.

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ First, factor the denominators and numerators where possible. The expression is: $$ \frac{x+3}{x^2 - 5x + 6} \cdot \frac{4x - 12}{x + 2} $$ ‖ ‖ step 2 ⋮ Factor the quadratic expression in the denominator: $$ x^2 - 5x + 6 = (x - 2)(x + 3) $$ ‖ ‖ step 3 ⋮ Substitute the factored form into the expression: $$ \frac{x+3}{(x-2)(x+3)} \cdot \frac{4x - 12}{x + 2} $$ ‖ ‖ step 4 ⋮ Simplify the numerator $4x - 12$: $$ 4x - 12 = 4(x - 3) $$ ‖ ‖ step 5 ⋮ Substitute the simplified numerator: $$ \frac{x+3}{(x-2)(x+3)} \cdot \frac{4(x - 3)}{x + 2} $$ ‖ ‖ step 6 ⋮ Cancel out the common factors $(x + 3)$: $$ \frac{1}{x-2} \cdot \frac{4(x - 3)}{x + 2} $$ ‖ ‖ step 7 ⋮ Multiply the remaining fractions: $$ \frac{4(x - 3)}{(x - 2)(x + 2)} $$ ‖ ‖ step 8 ⋮ Simplify the final expression: $$ \frac{4x - 12}{x^2 - 4} $$ ‖ ∻Answer∻ ⚹$\frac{4x - 12}{x^2 - 4}$⚹ ∻Key Concept∻ ⚹Simplification of Rational Expressions⚹ ∻Explanation∻ ⚹The key concept here is to factor both the numerator and the denominator where possible, cancel out common factors, and then simplify the resulting expression.⚹◊What is the simplified expression for $\frac{x+3}{x^{2}-5x+6} \cdot \frac{4x-12}{x+2}$⍭ Generate me a similar question◊

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