Solve p-p+2/4/frac{3{4}-5/2p}

$$\frac { p - \frac { p + 2 } { 4 } } { \frac { 3 } { 4 } - \frac { 5 } { 2 p } }$$

Evaluate

$$\frac{p\left(3p-2\right)}{3p-10}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply p times \frac{4}{4}.

$$\frac{\frac{4p}{4}-\frac{p+2}{4}}{\frac{3}{4}-\frac{5}{2p}}$$

Since \frac{4p}{4} and \frac{p+2}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{4p-\left(p+2\right)}{4}}{\frac{3}{4}-\frac{5}{2p}}$$

Do the multiplications in 4p-\left(p+2\right).

$$\frac{\frac{4p-p-2}{4}}{\frac{3}{4}-\frac{5}{2p}}$$

Combine like terms in 4p-p-2.

$$\frac{\frac{3p-2}{4}}{\frac{3}{4}-\frac{5}{2p}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4 and 2p is 4p. Multiply \frac{3}{4} times \frac{p}{p}. Multiply \frac{5}{2p} times \frac{2}{2}.

$$\frac{\frac{3p-2}{4}}{\frac{3p}{4p}-\frac{5\times 2}{4p}}$$

Since \frac{3p}{4p} and \frac{5\times 2}{4p} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{3p-2}{4}}{\frac{3p-5\times 2}{4p}}$$

Do the multiplications in 3p-5\times 2.

$$\frac{\frac{3p-2}{4}}{\frac{3p-10}{4p}}$$

Divide \frac{3p-2}{4} by \frac{3p-10}{4p} by multiplying \frac{3p-2}{4} by the reciprocal of \frac{3p-10}{4p}.

$$\frac{\left(3p-2\right)\times 4p}{4\left(3p-10\right)}$$

Cancel out 4 in both numerator and denominator.

$$\frac{p\left(3p-2\right)}{3p-10}$$

Use the distributive property to multiply p by 3p-2.

$$\frac{3p^{2}-2p}{3p-10}$$

Expand

$$\frac{3p^{2}-2p}{3p-10}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply p times \frac{4}{4}.

$$\frac{\frac{4p}{4}-\frac{p+2}{4}}{\frac{3}{4}-\frac{5}{2p}}$$

Since \frac{4p}{4} and \frac{p+2}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{4p-\left(p+2\right)}{4}}{\frac{3}{4}-\frac{5}{2p}}$$

Do the multiplications in 4p-\left(p+2\right).

$$\frac{\frac{4p-p-2}{4}}{\frac{3}{4}-\frac{5}{2p}}$$

Combine like terms in 4p-p-2.

$$\frac{\frac{3p-2}{4}}{\frac{3}{4}-\frac{5}{2p}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4 and 2p is 4p. Multiply \frac{3}{4} times \frac{p}{p}. Multiply \frac{5}{2p} times \frac{2}{2}.

$$\frac{\frac{3p-2}{4}}{\frac{3p}{4p}-\frac{5\times 2}{4p}}$$

Since \frac{3p}{4p} and \frac{5\times 2}{4p} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{3p-2}{4}}{\frac{3p-5\times 2}{4p}}$$

Do the multiplications in 3p-5\times 2.

$$\frac{\frac{3p-2}{4}}{\frac{3p-10}{4p}}$$

Divide \frac{3p-2}{4} by \frac{3p-10}{4p} by multiplying \frac{3p-2}{4} by the reciprocal of \frac{3p-10}{4p}.

$$\frac{\left(3p-2\right)\times 4p}{4\left(3p-10\right)}$$

Cancel out 4 in both numerator and denominator.

$$\frac{p\left(3p-2\right)}{3p-10}$$

Use the distributive property to multiply p by 3p-2.

$$\frac{3p^{2}-2p}{3p-10}$$