Question

\(\frac{3}{X+1}\)-\(\frac{2}{X+3}\)=\(\frac{4X+5}{X^2+4X+3}\)

Answer 1

\(\frac{3}{x+1}-\frac{2}{x+3}=\frac{4x+5}{x^2+4x+3}\)

\(\Leftrightarrow\frac{3}{x+1}-\frac{2}{x+3}=\frac{4x+5}{\left(x+1\right)\left(x+3\right)}\)

\(\Leftrightarrow3\left(x+3\right)-2\left(x+1\right)=4x+5\)

\(\Leftrightarrow x+7=4x+5\)

\(\Leftrightarrow7=4x+5-x\)

\(\Leftrightarrow7=3x+5\)

\(\Leftrightarrow7-5=3x\)

\(\Leftrightarrow2=3x\)

\(\Leftrightarrow\frac{2}{3}=x\)

\(\Rightarrow x=\frac{2}{3}\)