Question

Simplify: %29%7D" id="TexFormula1" title="\frac{1}{(x+3)(x+4)} +\frac{2}{(x+4)(x+5)}" alt="\frac{1}{(x+3)(x+4)} +\frac{2}{(x+4)(x+5)}" align="absmiddle" class="latex-formula">

Answer 1

Answer:

$\frac{3x+11}{(x+3)(x+4)(x+5)}$

Step-by-step explanation:

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

Multiplying the numerator/ denominator of the first fraction by (x + 5)

Multiplying the numerator/ denominator of the second fraction by (x + 3)

= $\frac{x+5}{(x+3)(x+4)(x+5)}$ + $\frac{2(x+3)}{(x+3)(x+4)(x+5)}$

Now add the numerators leaving the common denominator

= $\frac{x+5+2x+6}{(x+3)(x+4)(x+5)}$

= $\frac{3x+11}{(x+3)(x+4)(x+5)}$