Solve 1/a+1/b+1/c=1/4

$$\frac { 1 } { a } + \frac { 1 } { b } + \frac { 1 } { c } = \frac { 1 } { 4 }$$

Solve for a

$$a=-\frac{4bc}{4c+4b-bc}$$

$$b\neq 0\text{ and }c\neq 0\text{ and }\left(c=4\text{ or }b\neq -\frac{4c}{4-c}\right)$$

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 4abc, the least common multiple of a,b,c,4.

$$4bc+4ac+4ab=abc$$

Subtract abc from both sides.

$$4bc+4ac+4ab-abc=0$$

Subtract 4bc from both sides. Anything subtracted from zero gives its negation.

$$4ac+4ab-abc=-4bc$$

Combine all terms containing a.

$$\left(4c+4b-bc\right)a=-4bc$$

Divide both sides by 4b+4c-bc.

$$\frac{\left(4c+4b-bc\right)a}{4c+4b-bc}=-\frac{4bc}{4c+4b-bc}$$

Dividing by 4b+4c-bc undoes the multiplication by 4b+4c-bc.

$$a=-\frac{4bc}{4c+4b-bc}$$

Variable a cannot be equal to 0.

$$a=-\frac{4bc}{4c+4b-bc}\text{, }a\neq 0$$

Solve for b

$$b=-\frac{4ac}{4c+4a-ac}$$

$$a\neq 0\text{ and }c\neq 0\text{ and }\left(c=4\text{ or }a\neq -\frac{4c}{4-c}\right)$$

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 4abc, the least common multiple of a,b,c,4.

$$4bc+4ac+4ab=abc$$

Subtract abc from both sides.

$$4bc+4ac+4ab-abc=0$$

Subtract 4ac from both sides. Anything subtracted from zero gives its negation.

$$4bc+4ab-abc=-4ac$$

Combine all terms containing b.

$$\left(4c+4a-ac\right)b=-4ac$$

Divide both sides by 4a+4c-ac.

$$\frac{\left(4c+4a-ac\right)b}{4c+4a-ac}=-\frac{4ac}{4c+4a-ac}$$

Dividing by 4a+4c-ac undoes the multiplication by 4a+4c-ac.

$$b=-\frac{4ac}{4c+4a-ac}$$

Variable b cannot be equal to 0.

$$b=-\frac{4ac}{4c+4a-ac}\text{, }b\neq 0$$