Express as a single fraction in its simplest form: 3 3/4 − 2 1/2

Question

ScanSolve AI Tutor · Accepted Answer

Here's how to express the given expression as a single fraction:

Find a common denominator for the two fractions.
The denominators are $(a-4)$ and 2. The least common denominator is $2(a-4)$ .
Rewrite each fraction with the common denominator.
$\frac{2a-5}{a-4} = \frac{(2a-5) \times 2}{(a-4) \times 2} = \frac{2(2a-5)}{2(a-4)}$ $\frac{1}{2} = \frac{1 \times (a-4)}{2 \times (a-4)} = \frac{a-4}{2(a-4)}$
Perform the subtraction.
$\frac{2(2a-5)}{2(a-4)} - \frac{a-4}{2(a-4)} = \frac{2(2a-5) - (a-4)}{2(a-4)}$
Expand the numerator and simplify.
$\frac{4a - 10 - a + 4}{2(a-4)} = \frac{3a - 6}{2(a-4)}$
Factor out any common terms in the numerator if possible.
$\frac{3(a - 2)}{2(a-4)}$

Express as a single fraction in its simplest form: 3 3/4 - 2 1/2