Help me with algebra!!

Question

Rational Expression: show how to simplify the following rational expression.show all steps. >> (sq rt of x-4)=(sq rt of 2x+2)+1

Answer 1

First we square both sides:

√(x-4)•√(x-4) = (√(2x+2) + 1)(√(2x+2) + 1)

x-4 = 2x+2 + √(2x+2) + √(2x+2) + 1

x-4 = 2x + 2√(2x+2) + 3

subtract 3 from both sides and 2x from both sides

-x-7 = 2√(2x+2)

square both sides

(-x-7)(-x-7) = (2√(2x+2))(2√(2x+2))

x² + 7x + 7x + 49 = 4(2x+2)

subtract 8x from both sides and 8 from both sides

x² + 6x + 41 = 0

then we use the quadratic equation:

-6 ± √(6² - 4(1)(41))/2

simplifies to

-3 ± 4√2i