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

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

Solve for c

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

Steps for Solving Linear Equation

Variable c 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(c+1\right)\left(c+3\right), the least common multiple of 2c+2,c+3,2c+6.

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

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

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

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

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

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

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

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

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

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

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

Add -6 and 2 to get -4.

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

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

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

Subtract 5c^{2} from both sides.

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

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

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

Subtract 20c from both sides.

$$27c-4-20c=15$$

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

$$7c-4=15$$

Add 4 to both sides.

$$7c=15+4$$

Add 15 and 4 to get 19.

$$7c=19$$

Divide both sides by 7.

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