Answer:
[tex] \frac{5 {x}^{2} + 5x + 3 }{3 {x}^{2} + 3x} [/tex]
Step-by-step explanation:
[tex] \frac{2x + 3}{3x} + \frac{x}{ x + 1} [/tex]
Write all the numerators above the least common denominator
[tex] \frac{(x + 1)(2x + 3) + 3 {x}^{2} }{3x(x + 1)} [/tex]
Multiply the parentheses
[tex] \frac{2 {x}^{2} + 3x + 2x + 3 + 3 {x}^{2} }{3x(x + 1)} [/tex]
Distribute 3x through the parentheses
[tex] \frac{2 {x}^{2} + 3x + 2x + 3 + 3 {x}^{2} }{3 {x}^{2} + 3x} [/tex]
Collect like terms[tex] =
\frac{5 {x}^{2} + 5x + 3 }{3 {x}^{2} + 3 x} [/tex]
Hope this helps...
Good luck on your assignment...
