Question

Add the rational expressions and type your answer in simplest form, multiplying any factors you may have in the numerator or denominator. When typing your answers, type your terms with variables in descending power and in alphabetical order without any spaces between your characters. If needed use the carrot key ^ (press shift and 6) to indicate an exponent. \frac{4}{a+1} + \frac{5}{a-3}

Answer 1

Given:

The expression is,

`(4)/(a+1)+(5)/(a-3)`

Simpify the expression,

`\begin{gathered} (4)/(a+1)+(5)/(a-3) \\ \text{Adjust fractions based on least common multiple,} \\ =(4\left(a-3\right))/(\left(a+1\right)\left(a-3\right))+(5\left(a+1\right))/(\left(a+1\right)\left(a-3\right)) \\ =(4(a-3)+5\mleft(a+1\mright))/((a+1)(a-3)) \\ =(4a-12+5a+5)/((a+1)(a-3)) \\ =(9a-7)/((a+1)(a-3)) \end{gathered}`

Answer:

`\begin{gathered} \text{Numerator}=\text{ 9a-7} \\ \text{Denominator}=\text{ (a+1)(a-3)} \end{gathered}`