Solve p-2/p+1/1-frac{4p+7{p^2+4p+3}}

$$\frac { p - \frac { 2 } { p + 1 } } { 1 - \frac { 4 p + 7 } { p ^ { 2 } + 4 p + 3 } }$$

Evaluate

$$\frac{\left(p-1\right)\left(p+3\right)}{p-2}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply p times \frac{p+1}{p+1}.

$$\frac{\frac{p\left(p+1\right)}{p+1}-\frac{2}{p+1}}{1-\frac{4p+7}{p^{2}+4p+3}}$$

Since \frac{p\left(p+1\right)}{p+1} and \frac{2}{p+1} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{p\left(p+1\right)-2}{p+1}}{1-\frac{4p+7}{p^{2}+4p+3}}$$

Do the multiplications in p\left(p+1\right)-2.

$$\frac{\frac{p^{2}+p-2}{p+1}}{1-\frac{4p+7}{p^{2}+4p+3}}$$

Factor p^{2}+4p+3.

$$\frac{\frac{p^{2}+p-2}{p+1}}{1-\frac{4p+7}{\left(p+1\right)\left(p+3\right)}}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{\left(p+1\right)\left(p+3\right)}{\left(p+1\right)\left(p+3\right)}.

$$\frac{\frac{p^{2}+p-2}{p+1}}{\frac{\left(p+1\right)\left(p+3\right)}{\left(p+1\right)\left(p+3\right)}-\frac{4p+7}{\left(p+1\right)\left(p+3\right)}}$$

Since \frac{\left(p+1\right)\left(p+3\right)}{\left(p+1\right)\left(p+3\right)} and \frac{4p+7}{\left(p+1\right)\left(p+3\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{p^{2}+p-2}{p+1}}{\frac{\left(p+1\right)\left(p+3\right)-\left(4p+7\right)}{\left(p+1\right)\left(p+3\right)}}$$

Do the multiplications in \left(p+1\right)\left(p+3\right)-\left(4p+7\right).

$$\frac{\frac{p^{2}+p-2}{p+1}}{\frac{p^{2}+3p+3+p-4p-7}{\left(p+1\right)\left(p+3\right)}}$$

Combine like terms in p^{2}+3p+3+p-4p-7.

$$\frac{\frac{p^{2}+p-2}{p+1}}{\frac{p^{2}-4}{\left(p+1\right)\left(p+3\right)}}$$

Divide \frac{p^{2}+p-2}{p+1} by \frac{p^{2}-4}{\left(p+1\right)\left(p+3\right)} by multiplying \frac{p^{2}+p-2}{p+1} by the reciprocal of \frac{p^{2}-4}{\left(p+1\right)\left(p+3\right)}.

$$\frac{\left(p^{2}+p-2\right)\left(p+1\right)\left(p+3\right)}{\left(p+1\right)\left(p^{2}-4\right)}$$

Cancel out p+1 in both numerator and denominator.

$$\frac{\left(p+3\right)\left(p^{2}+p-2\right)}{p^{2}-4}$$

Factor the expressions that are not already factored.

$$\frac{\left(p-1\right)\left(p+2\right)\left(p+3\right)}{\left(p-2\right)\left(p+2\right)}$$

Cancel out p+2 in both numerator and denominator.

$$\frac{\left(p-1\right)\left(p+3\right)}{p-2}$$

Expand the expression.

$$\frac{p^{2}+2p-3}{p-2}$$

Expand

$$\frac{p^{2}+2p-3}{p-2}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply p times \frac{p+1}{p+1}.

$$\frac{\frac{p\left(p+1\right)}{p+1}-\frac{2}{p+1}}{1-\frac{4p+7}{p^{2}+4p+3}}$$

Since \frac{p\left(p+1\right)}{p+1} and \frac{2}{p+1} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{p\left(p+1\right)-2}{p+1}}{1-\frac{4p+7}{p^{2}+4p+3}}$$

Do the multiplications in p\left(p+1\right)-2.

$$\frac{\frac{p^{2}+p-2}{p+1}}{1-\frac{4p+7}{p^{2}+4p+3}}$$

Factor p^{2}+4p+3.

$$\frac{\frac{p^{2}+p-2}{p+1}}{1-\frac{4p+7}{\left(p+1\right)\left(p+3\right)}}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{\left(p+1\right)\left(p+3\right)}{\left(p+1\right)\left(p+3\right)}.

$$\frac{\frac{p^{2}+p-2}{p+1}}{\frac{\left(p+1\right)\left(p+3\right)}{\left(p+1\right)\left(p+3\right)}-\frac{4p+7}{\left(p+1\right)\left(p+3\right)}}$$

Since \frac{\left(p+1\right)\left(p+3\right)}{\left(p+1\right)\left(p+3\right)} and \frac{4p+7}{\left(p+1\right)\left(p+3\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{p^{2}+p-2}{p+1}}{\frac{\left(p+1\right)\left(p+3\right)-\left(4p+7\right)}{\left(p+1\right)\left(p+3\right)}}$$

Do the multiplications in \left(p+1\right)\left(p+3\right)-\left(4p+7\right).

$$\frac{\frac{p^{2}+p-2}{p+1}}{\frac{p^{2}+3p+3+p-4p-7}{\left(p+1\right)\left(p+3\right)}}$$

Combine like terms in p^{2}+3p+3+p-4p-7.

$$\frac{\frac{p^{2}+p-2}{p+1}}{\frac{p^{2}-4}{\left(p+1\right)\left(p+3\right)}}$$

Divide \frac{p^{2}+p-2}{p+1} by \frac{p^{2}-4}{\left(p+1\right)\left(p+3\right)} by multiplying \frac{p^{2}+p-2}{p+1} by the reciprocal of \frac{p^{2}-4}{\left(p+1\right)\left(p+3\right)}.

$$\frac{\left(p^{2}+p-2\right)\left(p+1\right)\left(p+3\right)}{\left(p+1\right)\left(p^{2}-4\right)}$$

Cancel out p+1 in both numerator and denominator.

$$\frac{\left(p+3\right)\left(p^{2}+p-2\right)}{p^{2}-4}$$

Factor the expressions that are not already factored.

$$\frac{\left(p-1\right)\left(p+2\right)\left(p+3\right)}{\left(p-2\right)\left(p+2\right)}$$

Cancel out p+2 in both numerator and denominator.

$$\frac{\left(p-1\right)\left(p+3\right)}{p-2}$$

Expand the expression.

$$\frac{p^{2}+2p-3}{p-2}$$