Solve 1+10/4+frac{3{x+1}}=3

$$1 + \frac { 10 } { 4 + \frac { 3 } { x + 1 } } = 3$$

Solve for x

$$x=2$$

Steps for Solving Linear Equation

To add or subtract expressions, expand them to make their denominators the same. Multiply 4 times \frac{x+1}{x+1}.

$$1+\frac{10}{\frac{4\left(x+1\right)}{x+1}+\frac{3}{x+1}}=3$$

Since \frac{4\left(x+1\right)}{x+1} and \frac{3}{x+1} have the same denominator, add them by adding their numerators.

$$1+\frac{10}{\frac{4\left(x+1\right)+3}{x+1}}=3$$

Do the multiplications in 4\left(x+1\right)+3.

$$1+\frac{10}{\frac{4x+4+3}{x+1}}=3$$

Combine like terms in 4x+4+3.

$$1+\frac{10}{\frac{4x+7}{x+1}}=3$$

Variable x cannot be equal to -1 since division by zero is not defined. Divide 10 by \frac{4x+7}{x+1} by multiplying 10 by the reciprocal of \frac{4x+7}{x+1}.

$$1+\frac{10\left(x+1\right)}{4x+7}=3$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{4x+7}{4x+7}.

$$\frac{4x+7}{4x+7}+\frac{10\left(x+1\right)}{4x+7}=3$$

Since \frac{4x+7}{4x+7} and \frac{10\left(x+1\right)}{4x+7} have the same denominator, add them by adding their numerators.

$$\frac{4x+7+10\left(x+1\right)}{4x+7}=3$$

Do the multiplications in 4x+7+10\left(x+1\right).

$$\frac{4x+7+10x+10}{4x+7}=3$$

Combine like terms in 4x+7+10x+10.

$$\frac{14x+17}{4x+7}=3$$

Variable x cannot be equal to -\frac{7}{4} since division by zero is not defined. Multiply both sides of the equation by 4x+7.

$$14x+17=3\left(4x+7\right)$$

Use the distributive property to multiply 3 by 4x+7.

$$14x+17=12x+21$$

Subtract 12x from both sides.

$$14x+17-12x=21$$

Combine 14x and -12x to get 2x.

$$2x+17=21$$

Subtract 17 from both sides.

$$2x=21-17$$

Subtract 17 from 21 to get 4.

$$2x=4$$

Divide both sides by 2.

$$x=\frac{4}{2}$$

Divide 4 by 2 to get 2.

$$x=2$$