Problem 43
Question
Add or subtract as indicated. Simplify the result, if possible. $$\frac{7}{x-1}-\frac{3}{(x-1)^{2}}$$
Step-by-Step Solution
Verified Answer
The simplified form of the expression is \(\frac{7x-10}{(x-1)^2}\).
1Step 1: 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., \((x-1)\).
2Step 2: Rewrite the Fraction
Rewrite the second fraction as \(\frac{3}{(x-1) * (x-1)}\) which equals to \(\frac{3/(x-1)}{x-1}\).
3Step 3: 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 \(\frac{7x-10}{(x-1)^2}\).
Other exercises in this chapter
Problem 43
Simplify each rational expression. If the rational expression cannot be simplified, so state. $$\frac{2 y^{2}-7 y+3}{2 y^{2}-5 y+2}$$
View solution Problem 43
Simplify complex rational expression. \(\frac{y^{-1}-(y+5)^{-1}}{5}\)
View solution Problem 43
Divide as indicated. $$\frac{x^{2}-4}{x} \div \frac{x+2}{x-2}$$
View solution Problem 43
Solve each rational equation. $$\frac{1}{x-4}-\frac{5}{x+2}=\frac{6}{x^{2}-2 x-8}$$
View solution