SATMathematics Practice Test 1

To rewrite $\frac{1}{\frac{1}{\mathit{x}+2}+\frac{1}{\mathit{x}+3}}$,

multiply by $\frac{\left(\mathit{x}+2\right)\left(\mathit{x}+3\right)}{\left(\mathit{x}+2\right)\left(\mathit{x}+3\right)}$
This result in the expression $\frac{\left(\mathit{x}+2\right)\left(\mathit{x}+3\right)}{\left(\mathit{x}+3\right)\left(\mathit{x}+2\right)}$ , which is equivalent to the expression in choice B.
Choices A, C, and D are incorrect and could be the result of common algebraic errors that arise while manipulating a complex fraction.