Question

Combine the following fractions and express in fully reduced form.
start fraction, minus, 3, x, plus, 2, divided by, 4, x, plus, 3, end fraction, minus, start fraction, 2, x, minus, 5, divided by, 4, x, plus, 3, end fraction
4x+3
−3x+2
​
−
4x+3
2x−5

Answer 1

Both fractions have the same denominator, so subtract numerators:

(-3x + 2) - (2x - 5) = -3x + 2 - 2x + 5 = -5x + 7.

Thus the result is (-5x + 7)/(4x + 3), or equivalently (7 - 5x)/(4x + 3). (Domain: x ≠ -3/4.)