Solve 8/17-3/17y-9/10--3/10

$$\frac { 8 } { 17 } - \frac { 3 } { 17 } y \frac { - 9 } { 10 } - \frac { - 3 } { 10 }$$

Evaluate

$$\frac{27y+131}{170}$$

Solution Steps

Fraction \frac{-9}{10} can be rewritten as -\frac{9}{10} by extracting the negative sign.

$$\frac{8}{17}-\frac{3}{17}y\left(-\frac{9}{10}\right)-\frac{-3}{10}$$

Multiply \frac{3}{17} times -\frac{9}{10} by multiplying numerator times numerator and denominator times denominator.

$$\frac{8}{17}-\frac{3\left(-9\right)}{17\times 10}y-\frac{-3}{10}$$

Do the multiplications in the fraction \frac{3\left(-9\right)}{17\times 10}.

$$\frac{8}{17}-\frac{-27}{170}y-\frac{-3}{10}$$

Fraction \frac{-27}{170} can be rewritten as -\frac{27}{170} by extracting the negative sign.

$$\frac{8}{17}-\left(-\frac{27}{170}y\right)-\frac{-3}{10}$$

The opposite of -\frac{27}{170}y is \frac{27}{170}y.

$$\frac{8}{17}+\frac{27}{170}y-\frac{-3}{10}$$

Fraction \frac{-3}{10} can be rewritten as -\frac{3}{10} by extracting the negative sign.

$$\frac{8}{17}+\frac{27}{170}y-\left(-\frac{3}{10}\right)$$

The opposite of -\frac{3}{10} is \frac{3}{10}.

$$\frac{8}{17}+\frac{27}{170}y+\frac{3}{10}$$

Least common multiple of 17 and 10 is 170. Convert \frac{8}{17} and \frac{3}{10} to fractions with denominator 170.

$$\frac{80}{170}+\frac{27}{170}y+\frac{51}{170}$$

Since \frac{80}{170} and \frac{51}{170} have the same denominator, add them by adding their numerators.

$$\frac{80+51}{170}+\frac{27}{170}y$$

Add 80 and 51 to get 131.

$$\frac{131}{170}+\frac{27}{170}y$$

Factor

$$\frac{27y+131}{170}$$

Solution Steps

Factor out \frac{1}{170}.

$$\frac{131+27y}{170}$$

Consider 80+27y+51. Multiply and combine like terms.

$$27y+131$$

Rewrite the complete factored expression.

$$\frac{27y+131}{170}$$