Solve 1/a_{2}+1/4+1/a_{4}=7/8

$$\frac { 1 } { a _ { 2 } } + \frac { 1 } { 4 } + \frac { 1 } { a _ { 4 } } = \frac { 7 } { 8 }$$

Solve for a_2

$$a_{2}=-\frac{8a_{4}}{8-5a_{4}}$$

$$a_{4}\neq 0\text{ and }a_{4}\neq \frac{8}{5}$$

Steps for Solving Linear Equation

Variable a_{2} cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 8a_{2}a_{4}, the least common multiple of a_{2},4,a_{4},8.

$$8a_{4}+8a_{2}a_{4}\times \frac{1}{4}+8a_{2}=7a_{2}a_{4}$$

Multiply 8 and \frac{1}{4} to get 2.

$$8a_{4}+2a_{2}a_{4}+8a_{2}=7a_{2}a_{4}$$

Subtract 7a_{2}a_{4} from both sides.

$$8a_{4}+2a_{2}a_{4}+8a_{2}-7a_{2}a_{4}=0$$

Combine 2a_{2}a_{4} and -7a_{2}a_{4} to get -5a_{2}a_{4}.

$$8a_{4}-5a_{2}a_{4}+8a_{2}=0$$

Subtract 8a_{4} from both sides. Anything subtracted from zero gives its negation.

$$-5a_{2}a_{4}+8a_{2}=-8a_{4}$$

Combine all terms containing a_{2}.

$$\left(-5a_{4}+8\right)a_{2}=-8a_{4}$$

The equation is in standard form.

$$\left(8-5a_{4}\right)a_{2}=-8a_{4}$$

Divide both sides by 8-5a_{4}.

$$\frac{\left(8-5a_{4}\right)a_{2}}{8-5a_{4}}=-\frac{8a_{4}}{8-5a_{4}}$$

Dividing by 8-5a_{4} undoes the multiplication by 8-5a_{4}.

$$a_{2}=-\frac{8a_{4}}{8-5a_{4}}$$

Variable a_{2} cannot be equal to 0.

$$a_{2}=-\frac{8a_{4}}{8-5a_{4}}\text{, }a_{2}\neq 0$$

Solve for a_4

$$a_{4}=-\frac{8a_{2}}{8-5a_{2}}$$

$$a_{2}\neq 0\text{ and }a_{2}\neq \frac{8}{5}$$

Steps for Solving Linear Equation

Variable a_{4} cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 8a_{2}a_{4}, the least common multiple of a_{2},4,a_{4},8.

$$8a_{4}+8a_{2}a_{4}\times \frac{1}{4}+8a_{2}=7a_{2}a_{4}$$

Multiply 8 and \frac{1}{4} to get 2.

$$8a_{4}+2a_{2}a_{4}+8a_{2}=7a_{2}a_{4}$$

Subtract 7a_{2}a_{4} from both sides.

$$8a_{4}+2a_{2}a_{4}+8a_{2}-7a_{2}a_{4}=0$$

Combine 2a_{2}a_{4} and -7a_{2}a_{4} to get -5a_{2}a_{4}.

$$8a_{4}-5a_{2}a_{4}+8a_{2}=0$$

Subtract 8a_{2} from both sides. Anything subtracted from zero gives its negation.

$$8a_{4}-5a_{2}a_{4}=-8a_{2}$$

Combine all terms containing a_{4}.

$$\left(8-5a_{2}\right)a_{4}=-8a_{2}$$

Divide both sides by 8-5a_{2}.

$$\frac{\left(8-5a_{2}\right)a_{4}}{8-5a_{2}}=-\frac{8a_{2}}{8-5a_{2}}$$

Dividing by 8-5a_{2} undoes the multiplication by 8-5a_{2}.

$$a_{4}=-\frac{8a_{2}}{8-5a_{2}}$$

Variable a_{4} cannot be equal to 0.

$$a_{4}=-\frac{8a_{2}}{8-5a_{2}}\text{, }a_{4}\neq 0$$