Question

Multiply and fully simplify please show work please

Answer 1

STEP1:

Simplify

`(x + 4)/(x - 2) \\`

Equation at the end of step1:

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

Factoring: x2 - 4

Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)

Proof : (A+B) • (A-B) =

A² - AB + BA - B² =

A² - AB + AB - B² =

A² - B²

Note : AB = BA is the commutative property of multiplication.

Note : - AB + AB equals zero and is therefore eliminated from the expression.

Check : 4 is the square of 2

Check : x2 is the square of x1

Factorization is : (x + 2) • (x - 2)

Polynomial Long Division :

2.2 Polynomial Long Division

Dividing : x + 2

("Dividend")

By : x ("Divisor")

dividend x + 2

- divisor * x⁰ x

remainder 2

Quotient : 1

Remainder : 2

Equation at the end of step 2:

`((x + 2) * (x - 2))/(x) * ((x + 4))/(x - 2) \\`

Cancel out (x-2) which appears on both sides of the fraction line.

Final result :

`⇒ ((x + 2) * (x + 4))/(x) \\`