Question

Algebra 2: multiplying and dividing rational expressionsText if u need any questions regarding my image.

Answer 1

Step 1

Given:

`(x+2)*\frac{(x-2)}{(x+2)_{}}/(x^2-4)/(x-6)`

Required: To simplify the problem.

Step 2

Apply PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction).

As a rule, we will move from left to right. This means we will multiply first before dividing.

Therefore for the first part

`(x+2)*\frac{(x-2)}{(x+2)_{}}=\text{ x-2}`

Hence we can write,

`(x-2)/(x^2-4)/(x-6)`

Step 3

Expand x²-4 using the difference of two squares.

`\begin{gathered} (a+b)^2=(a+b)(a-b) \\ \text{Hence,} \\ x^2-4=(x^2-2^2) \\ x^2-4=(x+2)(x-2) \end{gathered}`

Hence, we can write

`(x-2)/\frac{(x+2)(x-2)_{}}{x-6}`

Step 4

Simplify step 3

`\begin{gathered} =(x-2)*(x-6)/((x+2)(x-2)) \\ =(x-6)/(x+2) \end{gathered}`

Hence after simplification, the answer is

`(x-6)/(x+2)`