SOLUTION: Hi I need help with rational equations. The directions say to solve the equation choosing a method. 42. x/9-8/x=1/9 43. (x+42)/x = x If you can do these and explain them I

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Hi I need help with rational equations. The directions say to solve the equation choosing a method. 42. x/9-8/x=1/9 43. (x+42)/x = x If you can do these and explain them I      Log On


   

Question 75319This question is from textbook Algebra 1 Concepts and Skills
: Hi I need help with rational equations. The directions say to solve the equation choosing a method.
42. x/9-8/x=1/9
43. (x+42)/x = x
If you can do these and explain them I would very much appreiciate it.
Thank You! This question is from textbook Algebra 1 Concepts and Skills

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
42. x/9-8/x=1/9
x%2F9+-+8%2Fx = 1%2F9
:
We want to get rid of the denominators, 9x is a common denominator so multiply
each term in the equation by 9x, this will cancel out the denominators and
give you:
x*x - 9(8) = x
x^2 - 72 = x
:
Subtract x from both sides and you have a quadratic equation:
x^2 - x - 72 = 0
Easily factored to:
(x-9)(x+8) = 0
:
x =+9 and x = -8
:
Substitute both of these in the original equation to check our solutions
x = 9
9%2F9+-+8%2F9 = 1%2F9
x = -8
-8%2F9+-+%288%2F-8%29 = 1%2F9%29
-8%2F9+%2B+%288%2F8%29 = 1%2F9%29
-8%2F9+%2B+1 = 1%2F9%29
:
:
43. (x+42)/x = x
%28%28x%2B42%29%29%2Fx = x
:
Multiply equation by x, gets rid of the denominator and you have;
x + 42 = x^2
0 = x^2 -x - 42; another easily factored quadratic equation:
(x-7)(x+6) = 0
x = +7 and x = -6
:
You can check the solutions by substituting both values in the original eq