Solve 2=5/2q+2q/q+1

$$2 = \frac { 5 } { 2 q } + \frac { 2 q } { q + 1 }$$

Solve for q

$$q=-5$$

Steps for Solving Linear Equation

Variable q cannot be equal to any of the values -1,0 since division by zero is not defined. Multiply both sides of the equation by 2q\left(q+1\right), the least common multiple of 2q,q+1.

$$4q\left(q+1\right)=\left(q+1\right)\times 5+2q\times 2q$$

Multiply 2q and 2q to get \left(2q\right)^{2}.

$$4q\left(q+1\right)=\left(q+1\right)\times 5+\left(2q\right)^{2}$$

Use the distributive property to multiply 4q by q+1.

$$4q^{2}+4q=\left(q+1\right)\times 5+\left(2q\right)^{2}$$

Use the distributive property to multiply q+1 by 5.

$$4q^{2}+4q=5q+5+\left(2q\right)^{2}$$

Expand \left(2q\right)^{2}.

$$4q^{2}+4q=5q+5+2^{2}q^{2}$$

Calculate 2 to the power of 2 and get 4.

$$4q^{2}+4q=5q+5+4q^{2}$$

Subtract 5q from both sides.

$$4q^{2}+4q-5q=5+4q^{2}$$

Combine 4q and -5q to get -q.

$$4q^{2}-q=5+4q^{2}$$

Subtract 4q^{2} from both sides.

$$4q^{2}-q-4q^{2}=5$$

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

$$-q=5$$

Multiply both sides by -1.

$$q=-5$$