Solve 8/a+10/b=6

$$\frac { 8 } { a } + \frac { 10 } { b } = 6$$

Solve for a

$$a=-\frac{4b}{5-3b}$$

$$b\neq 0\text{ and }b\neq \frac{5}{3}$$

Steps for Solving Linear Equation

Variable a cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by ab, the least common multiple of a,b.

$$b\times 8+a\times 10=6ab$$

Subtract 6ab from both sides.

$$b\times 8+a\times 10-6ab=0$$

Subtract b\times 8 from both sides. Anything subtracted from zero gives its negation.

$$a\times 10-6ab=-b\times 8$$

Multiply -1 and 8 to get -8.

$$a\times 10-6ab=-8b$$

Combine all terms containing a.

$$\left(10-6b\right)a=-8b$$

Divide both sides by 10-6b.

$$\frac{\left(10-6b\right)a}{10-6b}=-\frac{8b}{10-6b}$$

Dividing by 10-6b undoes the multiplication by 10-6b.

$$a=-\frac{8b}{10-6b}$$

Divide -8b by 10-6b.

$$a=-\frac{4b}{5-3b}$$

Variable a cannot be equal to 0.

$$a=-\frac{4b}{5-3b}\text{, }a\neq 0$$

Solve for b

$$b=-\frac{5a}{4-3a}$$

$$a\neq 0\text{ and }a\neq \frac{4}{3}$$

Steps for Solving Linear Equation

Variable b cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by ab, the least common multiple of a,b.

$$b\times 8+a\times 10=6ab$$

Subtract 6ab from both sides.

$$b\times 8+a\times 10-6ab=0$$

Subtract a\times 10 from both sides. Anything subtracted from zero gives its negation.

$$b\times 8-6ab=-a\times 10$$

Multiply -1 and 10 to get -10.

$$b\times 8-6ab=-10a$$

Combine all terms containing b.

$$\left(8-6a\right)b=-10a$$

Divide both sides by 8-6a.

$$\frac{\left(8-6a\right)b}{8-6a}=-\frac{10a}{8-6a}$$

Dividing by 8-6a undoes the multiplication by 8-6a.

$$b=-\frac{10a}{8-6a}$$

Divide -10a by 8-6a.

$$b=-\frac{5a}{4-3a}$$

Variable b cannot be equal to 0.

$$b=-\frac{5a}{4-3a}\text{, }b\neq 0$$