Question

what is the sum of the rational expressions below
2x+3/3x (plus) x/x+1

Answer 1

\[\frac{2x+3}{3x}+\frac{x}{x+1}=\frac{(x+1)(2x+3)+3x\times x}{3x(x+1)}\]

Answer 2

now some algebra to multiply out and combine like terms. but that is the basic idea. denominator is
\[3x^2+3x\] numerator is
\[2x^2+3x+2x+3+3x^2\]
\[=5x^2+5x+3\] so "final answer is
\[\frac{5x^2+5x+3}{3x^2+3x}\] unless i made an algebra mistake