Solve 1/x+1+3/x+4=4/x+3

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

Solve for x

$$x=5$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -4,-3,-1 since division by zero is not defined. Multiply both sides of the equation by \left(x+1\right)\left(x+3\right)\left(x+4\right), the least common multiple of x+1,x+4,x+3.

$$\left(x+3\right)\left(x+4\right)+\left(x+1\right)\left(x+3\right)\times 3=\left(x+1\right)\left(x+4\right)\times 4$$

Use the distributive property to multiply x+3 by x+4 and combine like terms.

$$x^{2}+7x+12+\left(x+1\right)\left(x+3\right)\times 3=\left(x+1\right)\left(x+4\right)\times 4$$

Use the distributive property to multiply x+1 by x+3 and combine like terms.

$$x^{2}+7x+12+\left(x^{2}+4x+3\right)\times 3=\left(x+1\right)\left(x+4\right)\times 4$$

Use the distributive property to multiply x^{2}+4x+3 by 3.

$$x^{2}+7x+12+3x^{2}+12x+9=\left(x+1\right)\left(x+4\right)\times 4$$

Combine x^{2} and 3x^{2} to get 4x^{2}.

$$4x^{2}+7x+12+12x+9=\left(x+1\right)\left(x+4\right)\times 4$$

Combine 7x and 12x to get 19x.

$$4x^{2}+19x+12+9=\left(x+1\right)\left(x+4\right)\times 4$$

Add 12 and 9 to get 21.

$$4x^{2}+19x+21=\left(x+1\right)\left(x+4\right)\times 4$$

Use the distributive property to multiply x+1 by x+4 and combine like terms.

$$4x^{2}+19x+21=\left(x^{2}+5x+4\right)\times 4$$

Use the distributive property to multiply x^{2}+5x+4 by 4.

$$4x^{2}+19x+21=4x^{2}+20x+16$$

Subtract 4x^{2} from both sides.

$$4x^{2}+19x+21-4x^{2}=20x+16$$

Combine 4x^{2} and -4x^{2} to get 0.

$$19x+21=20x+16$$

Subtract 20x from both sides.

$$19x+21-20x=16$$

Combine 19x and -20x to get -x.

$$-x+21=16$$

Subtract 21 from both sides.

$$-x=16-21$$

Subtract 21 from 16 to get -5.

$$-x=-5$$

Multiply both sides by -1.

$$x=5$$