Solve 3+15/2+4{1+frac{3/a}}=8

$$3 + \frac { 15 } { 2 + \frac { 4 } { 1 + \frac { 3 } { a } } } = 8$$

Solve for a

$$a=1$$

Steps for Solving Linear Equation

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{a}{a}.

$$3+\frac{15}{2+\frac{4}{\frac{a}{a}+\frac{3}{a}}}=8$$

Since \frac{a}{a} and \frac{3}{a} have the same denominator, add them by adding their numerators.

$$3+\frac{15}{2+\frac{4}{\frac{a+3}{a}}}=8$$

Variable a cannot be equal to 0 since division by zero is not defined. Divide 4 by \frac{a+3}{a} by multiplying 4 by the reciprocal of \frac{a+3}{a}.

$$3+\frac{15}{2+\frac{4a}{a+3}}=8$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 2 times \frac{a+3}{a+3}.

$$3+\frac{15}{\frac{2\left(a+3\right)}{a+3}+\frac{4a}{a+3}}=8$$

Since \frac{2\left(a+3\right)}{a+3} and \frac{4a}{a+3} have the same denominator, add them by adding their numerators.

$$3+\frac{15}{\frac{2\left(a+3\right)+4a}{a+3}}=8$$

Do the multiplications in 2\left(a+3\right)+4a.

$$3+\frac{15}{\frac{2a+6+4a}{a+3}}=8$$

Combine like terms in 2a+6+4a.

$$3+\frac{15}{\frac{6a+6}{a+3}}=8$$

Variable a cannot be equal to -3 since division by zero is not defined. Divide 15 by \frac{6a+6}{a+3} by multiplying 15 by the reciprocal of \frac{6a+6}{a+3}.

$$3+\frac{15\left(a+3\right)}{6a+6}=8$$

Factor the expressions that are not already factored in \frac{15\left(a+3\right)}{6a+6}.

$$3+\frac{15\left(a+3\right)}{6\left(a+1\right)}=8$$

Cancel out 3 in both numerator and denominator.

$$3+\frac{5\left(a+3\right)}{2\left(a+1\right)}=8$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 3 times \frac{2\left(a+1\right)}{2\left(a+1\right)}.

$$\frac{3\times 2\left(a+1\right)}{2\left(a+1\right)}+\frac{5\left(a+3\right)}{2\left(a+1\right)}=8$$

Since \frac{3\times 2\left(a+1\right)}{2\left(a+1\right)} and \frac{5\left(a+3\right)}{2\left(a+1\right)} have the same denominator, add them by adding their numerators.

$$\frac{3\times 2\left(a+1\right)+5\left(a+3\right)}{2\left(a+1\right)}=8$$

Do the multiplications in 3\times 2\left(a+1\right)+5\left(a+3\right).

$$\frac{6a+6+5a+15}{2\left(a+1\right)}=8$$

Combine like terms in 6a+6+5a+15.

$$\frac{11a+21}{2\left(a+1\right)}=8$$

Use the distributive property to multiply 2 by a+1.

$$\frac{11a+21}{2a+2}=8$$

Variable a cannot be equal to -1 since division by zero is not defined. Multiply both sides of the equation by 2\left(a+1\right).

$$11a+21=16\left(a+1\right)$$

Use the distributive property to multiply 16 by a+1.

$$11a+21=16a+16$$

Subtract 16a from both sides.

$$11a+21-16a=16$$

Combine 11a and -16a to get -5a.

$$-5a+21=16$$

Subtract 21 from both sides.

$$-5a=16-21$$

Subtract 21 from 16 to get -5.

$$-5a=-5$$

Divide both sides by -5.

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

Divide -5 by -5 to get 1.

$$a=1$$