Solve 3-a/b/frac{1{b}+b}

$$\frac { 3 - \frac { a } { b } } { \frac { 1 } { b } + b }$$

Evaluate

$$\frac{3b-a}{b^{2}+1}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 3 times \frac{b}{b}.

$$\frac{\frac{3b}{b}-\frac{a}{b}}{\frac{1}{b}+b}$$

Since \frac{3b}{b} and \frac{a}{b} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{3b-a}{b}}{\frac{1}{b}+b}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply b times \frac{b}{b}.

$$\frac{\frac{3b-a}{b}}{\frac{1}{b}+\frac{bb}{b}}$$

Since \frac{1}{b} and \frac{bb}{b} have the same denominator, add them by adding their numerators.

$$\frac{\frac{3b-a}{b}}{\frac{1+bb}{b}}$$

Do the multiplications in 1+bb.

$$\frac{\frac{3b-a}{b}}{\frac{1+b^{2}}{b}}$$

Divide \frac{3b-a}{b} by \frac{1+b^{2}}{b} by multiplying \frac{3b-a}{b} by the reciprocal of \frac{1+b^{2}}{b}.

$$\frac{\left(3b-a\right)b}{b\left(1+b^{2}\right)}$$

Cancel out b in both numerator and denominator.

$$\frac{-a+3b}{b^{2}+1}$$

Expand

$$\frac{3b-a}{b^{2}+1}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 3 times \frac{b}{b}.

$$\frac{\frac{3b}{b}-\frac{a}{b}}{\frac{1}{b}+b}$$

Since \frac{3b}{b} and \frac{a}{b} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{3b-a}{b}}{\frac{1}{b}+b}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply b times \frac{b}{b}.

$$\frac{\frac{3b-a}{b}}{\frac{1}{b}+\frac{bb}{b}}$$

Since \frac{1}{b} and \frac{bb}{b} have the same denominator, add them by adding their numerators.

$$\frac{\frac{3b-a}{b}}{\frac{1+bb}{b}}$$

Do the multiplications in 1+bb.

$$\frac{\frac{3b-a}{b}}{\frac{1+b^{2}}{b}}$$

Divide \frac{3b-a}{b} by \frac{1+b^{2}}{b} by multiplying \frac{3b-a}{b} by the reciprocal of \frac{1+b^{2}}{b}.

$$\frac{\left(3b-a\right)b}{b\left(1+b^{2}\right)}$$

Cancel out b in both numerator and denominator.

$$\frac{-a+3b}{b^{2}+1}$$