Solve 8x+13/3(x-1)+3(2x+3)/2(1-x)+x/2(x-1)

$$\frac { 8 x + 13 } { 3 ( x - 1 ) } + \frac { 3 ( 2 x + 3 ) } { 2 ( 1 - x ) } + \frac { x } { 2 ( x - 1 ) }$$

Evaluate

$$\frac{1}{6}\approx 0.166666667$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3\left(x-1\right) and 2\left(1-x\right) is 6\left(x-1\right). Multiply \frac{8x+13}{3\left(x-1\right)} times \frac{2}{2}. Multiply \frac{3\left(2x+3\right)}{2\left(1-x\right)} times \frac{-3}{-3}.

$$\frac{2\left(8x+13\right)}{6\left(x-1\right)}+\frac{-3\times 3\left(2x+3\right)}{6\left(x-1\right)}+\frac{x}{2\left(x-1\right)}$$

Since \frac{2\left(8x+13\right)}{6\left(x-1\right)} and \frac{-3\times 3\left(2x+3\right)}{6\left(x-1\right)} have the same denominator, add them by adding their numerators.

$$\frac{2\left(8x+13\right)-3\times 3\left(2x+3\right)}{6\left(x-1\right)}+\frac{x}{2\left(x-1\right)}$$

Do the multiplications in 2\left(8x+13\right)-3\times 3\left(2x+3\right).

$$\frac{16x+26-18x-27}{6\left(x-1\right)}+\frac{x}{2\left(x-1\right)}$$

Combine like terms in 16x+26-18x-27.

$$\frac{-2x-1}{6\left(x-1\right)}+\frac{x}{2\left(x-1\right)}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 6\left(x-1\right) and 2\left(x-1\right) is 6\left(x-1\right). Multiply \frac{x}{2\left(x-1\right)} times \frac{3}{3}.

$$\frac{-2x-1}{6\left(x-1\right)}+\frac{3x}{6\left(x-1\right)}$$

Since \frac{-2x-1}{6\left(x-1\right)} and \frac{3x}{6\left(x-1\right)} have the same denominator, add them by adding their numerators.

$$\frac{-2x-1+3x}{6\left(x-1\right)}$$

Combine like terms in -2x-1+3x.

$$\frac{x-1}{6\left(x-1\right)}$$

Cancel out x-1 in both numerator and denominator.

$$\frac{1}{6}$$

Factor

$$\frac{1}{2 \cdot 3} = 0.16666666666666666$$