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Chapter 0: Problem 60

Simplify each complex rational expression. $$\frac{\frac{x}{4}-1}{x-4}$$

Short Answer

Expert verified
The simplified form of the complex rational expression is \( \frac{x}{4(x - 4)} - \frac{1}{x - 4} \)

Step by step solution

01

Rewrite the Expression

Rewrite the complex rational expression as a division problem. Hence, the expression becomes \( \frac{x}{4} - 1 梅 x - 4 \).
02

Multiply By the Reciprocal

To simplify this expression, find the reciprocal of the denominator and multiply the expression in the numerator by the reciprocal. The reciprocal of \( x - 4 \) is \( \frac{1}{x - 4} \), resulting to \( \left(\frac{x}{4} - 1\right) * \frac{1}{x - 4} \)
03

Simplify the Expression

Distribute \( \frac{1}{x - 4} \) to \( \frac{x}{4} \) and -1, leading to \( \frac{x}{4(x - 4)} - \frac{1}{x - 4} \).

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Most popular questions from this chapter

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. \(x^{4}-16\) is factored completely as \(\left(x^{2}+4\right)\left(x^{2}-4\right)\)

Why must \(a\) and \(b\) represent non negative numbers when we write \(\sqrt{a} \cdot \sqrt{b}=\sqrt{a b ?}\) Is it necessary to use this restriction in the case of \(\sqrt[3]{a} \cdot \sqrt[3]{b}=\sqrt[3]{a b} ?\) Explain.

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$ x^{3}-64-(x+4)\left(x^{2}+4 x-16\right) $$

If \(b^{A}=M N, b^{C}=M,\) and \(b^{D}=N,\) what is the relationship among \(A, C,\) and \(D ?\)

Simplify using properties of exponents. $$\frac{72 x^{\frac{3}{4}}}{9 x^{\frac{1}{3}}}$$
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