Solve 3n/(2n-1)^2-5/2n-1

$$\frac { 3 n } { ( 2 n - 1 ) ^ { 2 } } - \frac { 5 } { 2 n - 1 }$$

Evaluate

$$\frac{5-7n}{\left(2n-1\right)^{2}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(2n-1\right)^{2} and 2n-1 is \left(2n-1\right)^{2}. Multiply \frac{5}{2n-1} times \frac{2n-1}{2n-1}.

$$\frac{3n}{\left(2n-1\right)^{2}}-\frac{5\left(2n-1\right)}{\left(2n-1\right)^{2}}$$

Since \frac{3n}{\left(2n-1\right)^{2}} and \frac{5\left(2n-1\right)}{\left(2n-1\right)^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3n-5\left(2n-1\right)}{\left(2n-1\right)^{2}}$$

Do the multiplications in 3n-5\left(2n-1\right).

$$\frac{3n-10n+5}{\left(2n-1\right)^{2}}$$

Combine like terms in 3n-10n+5.

$$\frac{-7n+5}{\left(2n-1\right)^{2}}$$

Expand \left(2n-1\right)^{2}.

$$\frac{-7n+5}{4n^{2}-4n+1}$$

Expand

$$-\frac{7n-5}{\left(2n-1\right)^{2}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(2n-1\right)^{2} and 2n-1 is \left(2n-1\right)^{2}. Multiply \frac{5}{2n-1} times \frac{2n-1}{2n-1}.

$$\frac{3n}{\left(2n-1\right)^{2}}-\frac{5\left(2n-1\right)}{\left(2n-1\right)^{2}}$$

Since \frac{3n}{\left(2n-1\right)^{2}} and \frac{5\left(2n-1\right)}{\left(2n-1\right)^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3n-5\left(2n-1\right)}{\left(2n-1\right)^{2}}$$

Do the multiplications in 3n-5\left(2n-1\right).

$$\frac{3n-10n+5}{\left(2n-1\right)^{2}}$$

Combine like terms in 3n-10n+5.

$$\frac{-7n+5}{\left(2n-1\right)^{2}}$$

Expand \left(2n-1\right)^{2}.

$$\frac{-7n+5}{4n^{2}-4n+1}$$