Question
The simplest form of the expression $$\frac{{{p^2} - p}}{{2{p^3} + {p^2}}}$$ + $$\frac{{{p^2} - 1}}{{{p^2} + 3p}}$$ + $$\frac{{{p^2}}}{{p + 1}}$$ = ?
Answer: Option B
$$\frac{{{p^2} - p}}{{2{p^3} + {p^2}}} + \frac{{{p^2} - 1}}{{{p^2} + 3p}} + \frac{{{p^2}}}{{p + 1}}$$
In such type of question assume values of p
$$\eqalign{
& \therefore {\text{Let }}p = 1 \cr
& \therefore \frac{{1 - 1}}{{2 + 1}} + \frac{{1 - 1}}{{1 + 3}} + \frac{1}{{1 + 1}} \cr
& = 0 + 0 + \frac{1}{2} \cr
& = \frac{1}{2} \cr
& {\text{Now check option 'B'}} \cr
& \frac{1}{{2{p^2}}} = \frac{1}{2} \cr
& {\text{Hence the answer is option 'B'}} \cr} $$
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$$\frac{{{p^2} - p}}{{2{p^3} + {p^2}}} + \frac{{{p^2} - 1}}{{{p^2} + 3p}} + \frac{{{p^2}}}{{p + 1}}$$
In such type of question assume values of p
$$\eqalign{
& \therefore {\text{Let }}p = 1 \cr
& \therefore \frac{{1 - 1}}{{2 + 1}} + \frac{{1 - 1}}{{1 + 3}} + \frac{1}{{1 + 1}} \cr
& = 0 + 0 + \frac{1}{2} \cr
& = \frac{1}{2} \cr
& {\text{Now check option 'B'}} \cr
& \frac{1}{{2{p^2}}} = \frac{1}{2} \cr
& {\text{Hence the answer is option 'B'}} \cr} $$
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