Add and Subtract Rational Expressions with Unlike Denominators: example 8.48

Subtract: $\frac{5 c + 4}{c - 2} - 3 .$

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Subtract: $\frac{2 x + 1}{x - 7} - 3 .$

How did it go?


Write $3$ as $\frac{3}{1}$ to have 2 rational expressions.
Do the rational expressions have a common denominator? No.
Find the LCD of $c - 2$ and $1 .$ LCD = $c - 2 .$
Rewrite $\frac{3}{1}$ as an equivalent rational expression with the LCD.
Simplify.
Subtract the rational expressions.
Simplify.
Factor to check for common factors.
There are no common factors; the rational expression is simplified.


Write $3$ as $\frac{3}{1}$ to have 2 rational expressions.
Do the rational expressions have a common denominator? No.
Find the LCD of $c - 2$ and $1 .$ LCD = $c - 2 .$
Rewrite $\frac{3}{1}$ as an equivalent rational expression with the LCD.
Simplify.
Subtract the rational expressions.
Simplify.
Factor to check for common factors.
There are no common factors; the rational expression is simplified.