Solve 1/3a+1/5b=1/15.1/2a+frac{1}{3b}=frac{1}{12}

$$\frac { 1 } { 3 a } + \frac { 1 } { 5 b } = \frac { 1 } { 15 } . \frac { 1 } { 2 a } + \frac { 1 } { 3 b } = \frac { 1 } { 12 }$$

Solve for a

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

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

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 15ab, the least common multiple of 3a,5b,15.

$$5b+3a=ab$$

Subtract ab from both sides.

$$5b+3a-ab=0$$

Subtract 5b from both sides. Anything subtracted from zero gives its negation.

$$3a-ab=-5b$$

Combine all terms containing a.

$$\left(3-b\right)a=-5b$$

Divide both sides by 3-b.

$$\frac{\left(3-b\right)a}{3-b}=-\frac{5b}{3-b}$$

Dividing by 3-b undoes the multiplication by 3-b.

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

Variable a cannot be equal to 0.

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

Solve for b

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

$$a\neq 0\text{ and }a\neq 5$$

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 15ab, the least common multiple of 3a,5b,15.

$$5b+3a=ab$$

Subtract ab from both sides.

$$5b+3a-ab=0$$

Subtract 3a from both sides. Anything subtracted from zero gives its negation.

$$5b-ab=-3a$$

Combine all terms containing b.

$$\left(5-a\right)b=-3a$$

Divide both sides by 5-a.

$$\frac{\left(5-a\right)b}{5-a}=-\frac{3a}{5-a}$$

Dividing by 5-a undoes the multiplication by 5-a.

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

Variable b cannot be equal to 0.

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