Solve 11x-2/2x+2-3x-1/x+3=5x+15/2x+6

$$\frac { 11 x - 2 } { 2 x + 2 } - \frac { 3 x - 1 } { x + 3 } = \frac { 5 x + 15 } { 2 x + 6 }$$

Solve for x

$$x = \frac{19}{7} = 2\frac{5}{7} \approx 2.714285714$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -3,-1 since division by zero is not defined. Multiply both sides of the equation by 2\left(x+1\right)\left(x+3\right), the least common multiple of 2x+2,x+3,2x+6.

$$\left(x+3\right)\left(11x-2\right)-\left(2x+2\right)\left(3x-1\right)=\left(x+1\right)\left(5x+15\right)$$

Use the distributive property to multiply x+3 by 11x-2 and combine like terms.

$$11x^{2}+31x-6-\left(2x+2\right)\left(3x-1\right)=\left(x+1\right)\left(5x+15\right)$$

Use the distributive property to multiply 2x+2 by 3x-1 and combine like terms.

$$11x^{2}+31x-6-\left(6x^{2}+4x-2\right)=\left(x+1\right)\left(5x+15\right)$$

To find the opposite of 6x^{2}+4x-2, find the opposite of each term.

$$11x^{2}+31x-6-6x^{2}-4x+2=\left(x+1\right)\left(5x+15\right)$$

Combine 11x^{2} and -6x^{2} to get 5x^{2}.

$$5x^{2}+31x-6-4x+2=\left(x+1\right)\left(5x+15\right)$$

Combine 31x and -4x to get 27x.

$$5x^{2}+27x-6+2=\left(x+1\right)\left(5x+15\right)$$

Add -6 and 2 to get -4.

$$5x^{2}+27x-4=\left(x+1\right)\left(5x+15\right)$$

Use the distributive property to multiply x+1 by 5x+15 and combine like terms.

$$5x^{2}+27x-4=5x^{2}+20x+15$$

Subtract 5x^{2} from both sides.

$$5x^{2}+27x-4-5x^{2}=20x+15$$

Combine 5x^{2} and -5x^{2} to get 0.

$$27x-4=20x+15$$

Subtract 20x from both sides.

$$27x-4-20x=15$$

Combine 27x and -20x to get 7x.

$$7x-4=15$$

Add 4 to both sides.

$$7x=15+4$$

Add 15 and 4 to get 19.

$$7x=19$$

Divide both sides by 7.

$$x=\frac{19}{7}$$