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Chapter 7: Problem 117

Perform the indicated operations. Simplify the result, if possible. $$\left(\frac{1}{x+h}-\frac{1}{x}\right) \div h$$

Short Answer

Expert verified
\(-1/[x(x + h)]\)

Step by step solution

01

Simplify the Numerator

Before performing the division, simplify the numerator which is a complex fraction.The numerator \(\left(\frac{1}{x+h}-\frac{1}{x}\right)\) can be rewritten using a common denominator, which would be \(x(x + h)\). Rewrite the numerator as: \(\frac{x - (x+h)}{x(x + h)} = \frac{-h}{x(x + h)}\).
02

Perform the Division

Now perform the division by replacing the division operation with multiplication by the reciprocal of the denominator which is \(h\). So replace \(h\) with \(\frac{1}{h}\) and the expression becomes: \(\frac{-h}{x(x + h)} \times \frac{1}{h}\). Simplify the fraction by cancelling common factors, which results in: \(\frac{-1}{x(x + h)}\).

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Most popular questions from this chapter

denominators are opposites, or additive inverses. Add or subtract as indicated. Simplify the result, if possible. $$\frac{x^{2}}{x-3}+\frac{9}{3-x}$$

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Will help you prepare for the material covered in the next section. a. If \(y=k x\) find the value of \(k\) using \(x=2\) and \(y=64\) b. Substitute the value for \(k\) into \(y=k x\) and write the resulting equation. c. Use the equation from part (b) to find \(y\) when \(x=5\)

determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The difference between two rational expressions with the same denominator can always be simplified.
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