Solve 8/b-2+3b/2-bquad424x/3xy+2

$$\frac { 8 } { b - 2 } + \frac { 3 b } { 2 - b } \quad 42 \frac { 4 x } { 3 x y } + 2$$

Evaluate

$$\frac{2\left(by+2y-84b\right)}{y\left(b-2\right)}$$

Short Solution Steps

Cancel out x in both numerator and denominator.

$$\frac{8}{b-2}+\frac{3b}{2-b}\times 42\times \frac{4}{3y}+2$$

Express \frac{3b}{2-b}\times 42 as a single fraction.

$$\frac{8}{b-2}+\frac{3b\times 42}{2-b}\times \frac{4}{3y}+2$$

Multiply \frac{3b\times 42}{2-b} times \frac{4}{3y} by multiplying numerator times numerator and denominator times denominator.

$$\frac{8}{b-2}+\frac{3b\times 42\times 4}{\left(2-b\right)\times 3y}+2$$

Cancel out 3 in both numerator and denominator.

$$\frac{8}{b-2}+\frac{4\times 42b}{y\left(-b+2\right)}+2$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of b-2 and y\left(-b+2\right) is y\left(b-2\right). Multiply \frac{8}{b-2} times \frac{y}{y}. Multiply \frac{4\times 42b}{y\left(-b+2\right)} times \frac{-1}{-1}.

$$\frac{8y}{y\left(b-2\right)}+\frac{-4\times 42b}{y\left(b-2\right)}+2$$

Since \frac{8y}{y\left(b-2\right)} and \frac{-4\times 42b}{y\left(b-2\right)} have the same denominator, add them by adding their numerators.

$$\frac{8y-4\times 42b}{y\left(b-2\right)}+2$$

Do the multiplications in 8y-4\times 42b.

$$\frac{8y-168b}{y\left(b-2\right)}+2$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 2 times \frac{y\left(b-2\right)}{y\left(b-2\right)}.

$$\frac{8y-168b}{y\left(b-2\right)}+\frac{2y\left(b-2\right)}{y\left(b-2\right)}$$

Since \frac{8y-168b}{y\left(b-2\right)} and \frac{2y\left(b-2\right)}{y\left(b-2\right)} have the same denominator, add them by adding their numerators.

$$\frac{8y-168b+2y\left(b-2\right)}{y\left(b-2\right)}$$

Do the multiplications in 8y-168b+2y\left(b-2\right).

$$\frac{8y-168b+2yb-4y}{y\left(b-2\right)}$$

Combine like terms in 8y-168b+2yb-4y.

$$\frac{4y-168b+2yb}{y\left(b-2\right)}$$

Expand y\left(b-2\right).

$$\frac{4y-168b+2yb}{by-2y}$$

Factor

$$\frac{2\left(by+2y-84b\right)}{y\left(b-2\right)}$$