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Chapter 0: Problem 39

Add or subtract as indicated. $$\frac{x^{2}+3 x}{x^{2}+x-12}-\frac{x^{2}-12}{x^{2}+x-12}$$

Short Answer

Expert verified
The result of the addition/subtraction is \(\frac{3x + 12}{x^{2}+x-12}\).

Step by step solution

01

Identify the common denominator

The common denominator for these two fractions is \(x^{2}+x-12\). This simplifies the process, and it means that you do not have to find the least common denominator since it is already provided.
02

Subtract the numerators

Since the fractions have a common denominator, you can directly subtract the numerators. Do this by rewriting the expression to subtract the numerators from each other: \((x^{2}+3 x) - (x^{2} -12)\). This simplifies to \(3x + 12\).
03

Write the simplified numerator over the common denominator

The simplified fraction after subtracting the numerators becomes \(\frac{3x + 12}{x^{2}+x-12}\).
04

Simplify the fraction if possible

The fraction \(\frac{3x + 12}{x^{2}+x-12}\) cannot be simplified any further since the numerator and the denominator have no common factors.

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