Solve b+c/a-b+9/5

$$\frac{ b+c }{ a-b } + \frac{ 9 }{ 5 }$$

Evaluate

$$\frac{9a-4b+5c}{5\left(a-b\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of a-b and 5 is 5\left(a-b\right). Multiply \frac{b+c}{a-b} times \frac{5}{5}. Multiply \frac{9}{5} times \frac{a-b}{a-b}.

$$\frac{5\left(b+c\right)}{5\left(a-b\right)}+\frac{9\left(a-b\right)}{5\left(a-b\right)}$$

Since \frac{5\left(b+c\right)}{5\left(a-b\right)} and \frac{9\left(a-b\right)}{5\left(a-b\right)} have the same denominator, add them by adding their numerators.

$$\frac{5\left(b+c\right)+9\left(a-b\right)}{5\left(a-b\right)}$$

Do the multiplications in 5\left(b+c\right)+9\left(a-b\right).

$$\frac{5b+5c+9a-9b}{5\left(a-b\right)}$$

Combine like terms in 5b+5c+9a-9b.

$$\frac{-4b+5c+9a}{5\left(a-b\right)}$$

Expand 5\left(a-b\right).

$$\frac{-4b+5c+9a}{5a-5b}$$

Expand

$$\frac{9a-4b+5c}{5\left(a-b\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of a-b and 5 is 5\left(a-b\right). Multiply \frac{b+c}{a-b} times \frac{5}{5}. Multiply \frac{9}{5} times \frac{a-b}{a-b}.

$$\frac{5\left(b+c\right)}{5\left(a-b\right)}+\frac{9\left(a-b\right)}{5\left(a-b\right)}$$

Since \frac{5\left(b+c\right)}{5\left(a-b\right)} and \frac{9\left(a-b\right)}{5\left(a-b\right)} have the same denominator, add them by adding their numerators.

$$\frac{5\left(b+c\right)+9\left(a-b\right)}{5\left(a-b\right)}$$

Do the multiplications in 5\left(b+c\right)+9\left(a-b\right).

$$\frac{5b+5c+9a-9b}{5\left(a-b\right)}$$

Combine like terms in 5b+5c+9a-9b.

$$\frac{-4b+5c+9a}{5\left(a-b\right)}$$

Expand 5\left(a-b\right).

$$\frac{-4b+5c+9a}{5a-5b}$$