Solve 5/a+4/6+frac{6{b}}

$$\frac { \frac { 5 } { a } + 4 } { 6 + \frac { 6 } { b } }$$

Evaluate

$$\frac{b\left(4a+5\right)}{6a\left(b+1\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 4 times \frac{a}{a}.

$$\frac{\frac{5}{a}+\frac{4a}{a}}{6+\frac{6}{b}}$$

Since \frac{5}{a} and \frac{4a}{a} have the same denominator, add them by adding their numerators.

$$\frac{\frac{5+4a}{a}}{6+\frac{6}{b}}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 6 times \frac{b}{b}.

$$\frac{\frac{5+4a}{a}}{\frac{6b}{b}+\frac{6}{b}}$$

Since \frac{6b}{b} and \frac{6}{b} have the same denominator, add them by adding their numerators.

$$\frac{\frac{5+4a}{a}}{\frac{6b+6}{b}}$$

Divide \frac{5+4a}{a} by \frac{6b+6}{b} by multiplying \frac{5+4a}{a} by the reciprocal of \frac{6b+6}{b}.

$$\frac{\left(5+4a\right)b}{a\left(6b+6\right)}$$

Use the distributive property to multiply 5+4a by b.

$$\frac{5b+4ab}{a\left(6b+6\right)}$$

Use the distributive property to multiply a by 6b+6.

$$\frac{5b+4ab}{6ab+6a}$$

Expand

$$\frac{4ab+5b}{6a\left(b+1\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 4 times \frac{a}{a}.

$$\frac{\frac{5}{a}+\frac{4a}{a}}{6+\frac{6}{b}}$$

Since \frac{5}{a} and \frac{4a}{a} have the same denominator, add them by adding their numerators.

$$\frac{\frac{5+4a}{a}}{6+\frac{6}{b}}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 6 times \frac{b}{b}.

$$\frac{\frac{5+4a}{a}}{\frac{6b}{b}+\frac{6}{b}}$$

Since \frac{6b}{b} and \frac{6}{b} have the same denominator, add them by adding their numerators.

$$\frac{\frac{5+4a}{a}}{\frac{6b+6}{b}}$$

Divide \frac{5+4a}{a} by \frac{6b+6}{b} by multiplying \frac{5+4a}{a} by the reciprocal of \frac{6b+6}{b}.

$$\frac{\left(5+4a\right)b}{a\left(6b+6\right)}$$

Use the distributive property to multiply 5+4a by b.

$$\frac{5b+4ab}{a\left(6b+6\right)}$$

Use the distributive property to multiply a by 6b+6.

$$\frac{5b+4ab}{6ab+6a}$$