Question

How to subtract algebraic fractions

Answer 1

Answer:

$\frac{5x+16}{(x+4)(x+6)}$

Step-by-step explanation:

Before subtracting we require the fractions to have a common denominator.

The lowest common multiple of x + 4 and x + 6 is (x + 4)(x + 6)

Multiply the numerator/denominator of the first fraction by x + 6 and

multiply the numerator/denominator of the second fraction by x + 4

= $\frac{(x+2)(x+6)}{(x+4)(x+6)}$ - $\frac{(x-1)(x+4)}{(x+4)(x+6)}$

Expand the numerators and simplify leaving the denominator

= $\frac{x^2+8x+12-(x^2+3x-4)}{(x+4)(x+6)}$

= $\frac{x^2+8x+12-x^2-3x+4}{(x+4)(x+6)}$

= $\frac{5x+16}{(x+4)(x+6)}$