Question

Perform the following operations and prove closure.

Answer 1

\[\frac{x }{x+3 }+\frac{ x+2 }{x+5 }\]

\[\frac{ x(x+5)+(x+2)(x+3) }{ (x+3)(x+5) }\]

\[\frac{ x^2+5x+x^2+5x+6 }{ (x+3)(x+5) }\]

\[\frac{2x^2+10x+6 }{ (x+3)(x+5) }\]

\[\frac{2(x^2+5x+3) }{ (x+3)(x+5) }\]

Answer 2

Thank you @Nurali, could you help me with one more?

Answer 3

\[\frac{ 2 }{ x^2-9}-\frac{ 3x }{ x^2-5x+6 }\]

\[\frac{ 2(x^2-5x+6)-3x(x^2-9) }{ (x^2-9)(x^2-5x+6)}\]

\[\frac{ (2x^2-10x+12)-(3x^3-27x) }{ (x^2-9)(x^2-5x+6)}\]

\[\frac{ -3x^3+2x^2-17x+12 }{ (x^2-9)(x^2-5x+6)}\]

Answer 4

Thank you so much!! @Nurali

Answer 5

My Pleasure @mariacruz07