Solve 27n-45/18-54n+90/36

$$\frac { 27 n - 45 } { 18 } - \frac { 54 n + 90 } { 36 }$$

Evaluate

$$-5$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 18 and 36 is 36. Multiply \frac{27n-45}{18} times \frac{2}{2}.

$$\frac{2\left(27n-45\right)}{36}-\frac{54n+90}{36}$$

Since \frac{2\left(27n-45\right)}{36} and \frac{54n+90}{36} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2\left(27n-45\right)-\left(54n+90\right)}{36}$$

Do the multiplications in 2\left(27n-45\right)-\left(54n+90\right).

$$\frac{54n-90-54n-90}{36}$$

Combine like terms in 54n-90-54n-90.

$$\frac{-180}{36}$$

Divide -180 by 36 to get -5.

$$-5$$

Factor

$$-5$$

Solution Steps

Factor out \frac{1}{2}.

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

Simplify.

$$-5$$