Solve 6/8x-3/4y-5/6x-1+2/3y

$$\frac{ 6 }{ 8 } x- \frac{ 3 }{ 4 } y- \frac{ 5 }{ 6 } x-1+ \frac{ 2 }{ 3 } y$$

Evaluate

$$-\frac{x}{12}-\frac{y}{12}-1$$

Solution Steps

Reduce the fraction \frac{6}{8} to lowest terms by extracting and canceling out 2.

$$\frac{3}{4}x-\frac{3}{4}y-\frac{5}{6}x-1+\frac{2}{3}y$$

Combine \frac{3}{4}x and -\frac{5}{6}x to get -\frac{1}{12}x.

$$-\frac{1}{12}x-\frac{3}{4}y-1+\frac{2}{3}y$$

Combine -\frac{3}{4}y and \frac{2}{3}y to get -\frac{1}{12}y.

$$-\frac{1}{12}x-\frac{1}{12}y-1$$

Factor

$$\frac{-x-y-12}{12}$$

Solution Steps

Factor out \frac{1}{12}.

$$\frac{9x-9y-10x-12+8y}{12}$$

Consider 9x-9y-10x-12+8y. Multiply and combine like terms.

$$-x-y-12$$

Rewrite the complete factored expression.

$$\frac{-x-y-12}{12}$$