Solve A+5/4a+11/12=2/3a

$$\frac { A + 5 } { 4 a } + \frac { 11 } { 12 } = \frac { 2 } { 3 a }$$

Solve for A

$$A=\frac{-11a-7}{3}$$

$$a\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 12a, the least common multiple of 4a,12,3a.

$$3\left(A+5\right)+12a\times \frac{11}{12}=4\times 2$$

Use the distributive property to multiply 3 by A+5.

$$3A+15+12a\times \frac{11}{12}=4\times 2$$

Multiply 12 and \frac{11}{12} to get 11.

$$3A+15+11a=4\times 2$$

Multiply 4 and 2 to get 8.

$$3A+15+11a=8$$

Subtract 15 from both sides.

$$3A+11a=8-15$$

Subtract 15 from 8 to get -7.

$$3A+11a=-7$$

Subtract 11a from both sides.

$$3A=-7-11a$$

The equation is in standard form.

$$3A=-11a-7$$

Divide both sides by 3.

$$\frac{3A}{3}=\frac{-11a-7}{3}$$

Dividing by 3 undoes the multiplication by 3.

$$A=\frac{-11a-7}{3}$$

Solve for a

$$a=\frac{-3A-7}{11}$$

$$A\neq -\frac{7}{3}$$

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 12a, the least common multiple of 4a,12,3a.

$$3\left(A+5\right)+12a\times \frac{11}{12}=4\times 2$$

Use the distributive property to multiply 3 by A+5.

$$3A+15+12a\times \frac{11}{12}=4\times 2$$

Multiply 12 and \frac{11}{12} to get 11.

$$3A+15+11a=4\times 2$$

Multiply 4 and 2 to get 8.

$$3A+15+11a=8$$

Subtract 3A from both sides.

$$15+11a=8-3A$$

Subtract 15 from both sides.

$$11a=8-3A-15$$

Subtract 15 from 8 to get -7.

$$11a=-7-3A$$

The equation is in standard form.

$$11a=-3A-7$$

Divide both sides by 11.

$$\frac{11a}{11}=\frac{-3A-7}{11}$$

Dividing by 11 undoes the multiplication by 11.

$$a=\frac{-3A-7}{11}$$

Variable a cannot be equal to 0.

$$a=\frac{-3A-7}{11}\text{, }a\neq 0$$