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Chapter 7: Problem 43

Add or subtract as indicated. Simplify the result, if possible. $$\frac{7}{x-1}-\frac{3}{(x-1)^{2}}$$

Short Answer

Expert verified
The simplified form of the expression is \(\frac{7x-10}{(x-1)^2}\).

Step by step solution

01

Identify the Common Denominator

Observe that the denominator \((x-1)^2\) can be written as \((x-1) * (x-1)\). This fact aligns the denominator of the second fraction with the first fraction. We can then rewrite the second fraction to have the same denominator as the first fraction i.e., \((x-1)\).
02

Rewrite the Fraction

Rewrite the second fraction as \(\frac{3}{(x-1) * (x-1)}\) which equals to \(\frac{3/(x-1)}{x-1}\).
03

Perform the subtraction

Now we can subtract the two fractions as their denominators are same, \(\frac{7}{x-1}\) - \(\frac{3/(x-1)}{x-1}\). Which can be further simplified as \(\frac{7x-10}{(x-1)^2}\).

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