SOLUTION: Fill in the blanks: a) For the expression 1 over the square root of x-2 to have real value, the value of X must be __________ than ________. b) the LCD of 1 over x+1 and 3 over (

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Fill in the blanks: a) For the expression 1 over the square root of x-2 to have real value, the value of X must be __________ than ________. b) the LCD of 1 over x+1 and 3 over (      Log On


   

Question 36591: Fill in the blanks:
a) For the expression 1 over the square root of x-2 to have real value, the value of X must be __________ than ________.
b) the LCD of 1 over x+1 and 3 over (x-1) is 1 over x^2 - 1. True or false?
c) 2x^2 + 13x - 34 = (__x + __) (x-__)
d) The equation 1/2 - 3 over 2x + 5 = 3/4 is equivalent to 4x - 2 = 6x + 15. True or False?
Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
a) For the expression 1+%2Fsqrt%28x-2%29+ to have real value, the value of X must be GREATER than 2.

b) the LCD of 1 over x+1 and 3 over (x-1) is 1 over x^2 - 1. FALSE . THE LCD is %28x-1%29%2A%28x%2B1%29+=+x%5E2+-1, NOT 1%2F%28x%5E2-1%29

c) 2x^2 + 13x - 34 = (2x + 17) (x-2)

d) The equation 1%2F2+-+3+%2F%282x+%2B+5%29+=+3%2F4+ is equivalent to 4x+-+2+=+6x+%2B+15.This one is hard, because EQUIVALENT EQUATIONS are equations that have the same solution set. It is necessary to solve both equations and see if they have exactly the same solution.
1%2F2+-+3+%2F%282x+%2B+5%29+=+3%2F4+
Multiply both sides by the LCD which is 4(2x+5).

2%282x%2B5%29+-+12+=+3%282x%2B5%29+
4x+%2B+10+-+12+=+6x+%2B+15+
4x+-+2=+6x+%2B+15

NOW, notice!!! This is exactly the same equation as the other one that was given. Therefore, as long as the solution doesn't make a denominator zero, the solution set will be EQUIVALENT!! If you solve this equation the rest of the way, you will get -17+=+2x so x=+-17%2F2, which does NOT make any denominators zero, so the statement is TRUE!!

R^2 at SCC, (Grandfather of Caylyne!!)