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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 simple form of the expression is \(\frac{3x + 12}{x^{2}+x-12}\)

Step by step solution

01

Identify the Denominator

From the problem, it can be observed that both fractions have a common denominator: \(x^{2}+x-12\). This is useful because when adding or subtracting fractions with the same denominator, the denominator stays the same. The operation works on the numerator only.
02

Subtract Numerators

Since the denominators of the two fractions are the same, we can directly subtract the numerators. The subtraction of the numerators, \((x^{2}+3x)-(x^{2}-12)\), simplifies first to \(x^{2}+3x - x^{2} + 12\), which can be further simplified to \(3x + 12\).
03

Final Result

Substituting the result of subtracting the numerators into one of the fractions gives the result: \(\frac{3x + 12}{x^{2}+x-12}\)

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