Solve 8p^2+4p/4p^2-1div2p+1

$$\frac { 8 p ^ { 2 } + 4 p } { 4 p ^ { 2 } - 1 } \div 2 p + 1$$

Evaluate

$$\frac{2p^{2}+2p-1}{2p-1}$$

Short Solution Steps

Express \frac{\frac{8p^{2}+4p}{4p^{2}-1}}{2} as a single fraction.

$$\frac{8p^{2}+4p}{\left(4p^{2}-1\right)\times 2}p+1$$

Factor the expressions that are not already factored in \frac{8p^{2}+4p}{\left(4p^{2}-1\right)\times 2}.

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

Cancel out 2\left(2p+1\right) in both numerator and denominator.

$$\frac{2p}{2p-1}p+1$$

Express \frac{2p}{2p-1}p as a single fraction.

$$\frac{2pp}{2p-1}+1$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{2p-1}{2p-1}.

$$\frac{2pp}{2p-1}+\frac{2p-1}{2p-1}$$

Since \frac{2pp}{2p-1} and \frac{2p-1}{2p-1} have the same denominator, add them by adding their numerators.

$$\frac{2pp+2p-1}{2p-1}$$

Do the multiplications in 2pp+2p-1.

$$\frac{2p^{2}+2p-1}{2p-1}$$

Expand

$$\frac{2p^{2}+2p-1}{2p-1}$$

Short Solution Steps

Express \frac{\frac{8p^{2}+4p}{4p^{2}-1}}{2} as a single fraction.

$$\frac{8p^{2}+4p}{\left(4p^{2}-1\right)\times 2}p+1$$

Factor the expressions that are not already factored in \frac{8p^{2}+4p}{\left(4p^{2}-1\right)\times 2}.

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

Cancel out 2\left(2p+1\right) in both numerator and denominator.

$$\frac{2p}{2p-1}p+1$$

Express \frac{2p}{2p-1}p as a single fraction.

$$\frac{2pp}{2p-1}+1$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{2p-1}{2p-1}.

$$\frac{2pp}{2p-1}+\frac{2p-1}{2p-1}$$

Since \frac{2pp}{2p-1} and \frac{2p-1}{2p-1} have the same denominator, add them by adding their numerators.

$$\frac{2pp+2p-1}{2p-1}$$

Do the multiplications in 2pp+2p-1.

$$\frac{2p^{2}+2p-1}{2p-1}$$