Solve 2f-5/3h+9/4k-1/2f-28/5k+frac{5}{4}h

$$2 f - \frac { 5 } { 3 } h + \frac { 9 } { 4 } k - \frac { 1 } { 2 } f - \frac { 28 } { 5 } k + \frac { 5 } { 4 } h$$

Evaluate

$$\frac{3f}{2}-\frac{5h}{12}-\frac{67k}{20}$$

Solution Steps

Combine 2f and -\frac{1}{2}f to get \frac{3}{2}f.

$$\frac{3}{2}f-\frac{5}{3}h+\frac{9}{4}k-\frac{28}{5}k+\frac{5}{4}h$$

Combine \frac{9}{4}k and -\frac{28}{5}k to get -\frac{67}{20}k.

$$\frac{3}{2}f-\frac{5}{3}h-\frac{67}{20}k+\frac{5}{4}h$$

Combine -\frac{5}{3}h and \frac{5}{4}h to get -\frac{5}{12}h.

$$\frac{3}{2}f-\frac{5}{12}h-\frac{67}{20}k$$

Factor

$$\frac{90f-25h-201k}{60}$$

Solution Steps

Factor out \frac{1}{60}.

$$\frac{120f-100h+135k-30f-336k+75h}{60}$$

Consider 120f-100h+135k-30f-336k+75h. Multiply and combine like terms.

$$90f-25h-201k$$

Rewrite the complete factored expression.

$$\frac{90f-25h-201k}{60}$$