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Chapter 7: Problem 68

Simplify each rational expression. If the rational expression cannot be simplified, so state. $$\frac{9-15 x}{5 x^{2}-3 x}$$

Short Answer

Expert verified
The final simplified form of the expression is \(3/x\)

Step by step solution

01

Factorize the numerator

The numerator \(9-15x\) can be factorized if we take out the common factor -3, thus it becomes -3(3-5x).
02

Factorize the denominator

In the denominator \(5x^{2}-3x\), the common factor x can be factored out, which results in x(5x-3).
03

Simplify the rational expression

Now let's simplify the rational expression \(-3(3-5x) / x(5x-3)\) by reducing same terms from numerator and denominator. This gives \(-3(-1) / x(-1)\)
04

Final Simplification

Simplifying we get: \(3/x\) which is the final simplified form of the given expression.

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Most popular questions from this chapter

perform the indicated operation. Where possible, reduce the answer to its lowest terms. $$\text { Simplify: } \frac{(y+2) y-2 \cdot 4}{4 y(y+4)}$$

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 \(x=5\)

Will help you prepare for the material covered in the next section. If \(B=k W,\) find the value of \(k,\) in decimal form, using \(B=5\) and \(W=160\)

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