Answer:
[tex]x(x + 1)[/tex]
Step-by-step explanation:
[tex] \frac{2x + 1}{ \frac{1}{x} + \frac{1}{x + 1} } [/tex]
Make denominators same:
[tex] \frac{2x + 1}{ \frac{x + 1}{x(x + 1)} + \frac{x}{(x + 1)} } [/tex]
Add the numerators:
[tex] \frac{2x + 1}{ \frac{x + 1 + x}{x(x + 1)} } [/tex]
[tex] \frac{2x + 1}{\frac{2x + 1}{x(x + 1)} } [/tex]
Apply the rule:
[tex] \frac{a}{ \frac{b}{c} } = \frac{a \times c}{b} [/tex]
Therefore,
[tex] \frac{(2x + 1)\times x(x + 1))}{2x + 1} [/tex]
Cancel out common factor of 2x+1:
[tex]x(x + 1)[/tex]
