Question

How do I solve this problem? (x)/(2x+2)=(-2x)/(4x+4)+(2x-3)/(x+1)?

Answer 1

\[\begin{array}{l} \frac{x}{2 x+2}=\frac{2 x-3}{x+1}-\frac{2 x}{4 x+4} \\ \text{Write both sides as a single fraction:} \\ \frac{x}{2 (x+1)}=\frac{3 (x-2)}{2 (x+1)} \\ \text{Cross multiply:} \\ 2 x (x+1)=6 (x-2) (x+1) \\ \text{Expand out terms on both sides:} \\ 2 x^2+2 x=6 x^2-6 x-12 \\ \text{Subtract }\left(6 x^2-6 x-12\right)\text{ from both sides:} \\ -4 x^2+8 x+12=0 \\ \text{Solve the quadratic equation by completing the square:}\text{}\text{Divide both sides by }-4: \\ x^2-2 x-3=0 \\\end{array}\]