Algebraic fractions

 

Divide \[ \begin{align} &\frac{x^2+3x+2}{x-2} \quad \text {by} \quad \frac{x^2-4}{x+3} \end{align} \ \]

Invert the divisor and multiply the two fractions

\[ \begin{align} \frac{x^2+3x+2}{x-2} \div \frac{x^2-4}{x+3} &= \frac{x^2+3x+2}{x-2} \times \frac{x+3}{x^2-4} \end{align} \ \]

Multiply the numerators. Look for factors first.

\[ \begin{align} &= \frac{(x+2)(x+1)(x+3)}{(x-2) \times (x^2-4)} \end{align} \ \]

Multiply the denominators. Look for factors first.

\[ \begin{align} &= \frac{(x+2)(x+1)(x+3)}{(x-2)(x-2)(x+2)} \\ &= \frac{(x+1)(x+3)}{(x-2)^2} \end{align} \ \] After cancelling common factors in numerator and denominator

You will gain most benefit if you work through each problem first and then come back and check your work against the solution.

 

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Now You Try:

Divide \[ \begin{align} &\frac{x^2+5x+6}{x-3} \quad \text {by} \quad \frac{x^2-9}{x+3} \end{align} \ \]