I need Help with Algebra Rational Expression Please!?

Question

Problem one is X over X-3 minus 2 over X Simplify and subtract

Problem two Is 2 over x plus 3 = 9 over 2
Solve the equation.

Please help thank you!

Answer 1

The first one involves finding a common denominator:

x/(x - 3) - 2/x

The common denominator is x(x - 3). So from there, you'd have to multiply your first fraction by x/x and your second fraction by (x - 3)/(x - 3). It's the same procedure as combining fractions, only here it's with variables. So here goes:

x/(x - 3) - 2/x = x^2/x(x - 3) - 2(x - 3)/x(x - 3)
= (x^2 - 2(x - 3))/(x(x - 3))
= (x^2 - 2x + 6) / (x^2 - 3x)

Since nothing cancels out at this point, this is your answer.

For the second problem, simply cross multiply to get rid of the fractions:

2/(x + 3) = 9/2
4 = 9(x + 3)
4 = 9x + 27
-23 = 9x
x = -23/9

This depends on where that "plus 3" goes - if it goes in the denominator like I wrote it above, then that's your answer. But if it is separate, then the answer should be:

2/x + 3 = 9/2
2/x = 3/2
4 = 3x
x = 4/3

Answer 2

problem 1 the answer is x squared -2x+6 all over x(x-3)
problem 2 x=4/3

Answer 3

hi Connor, i m not sure abt the respond yet i've got tried to remedy it,its been 4 yrs now as quickly as I had final time solved this manner of element yet see atleast if u get some theory out of it.... answer:6-y ------------------ y^2-2y-24 6-y ------------------ y^2+6y-4y-24 6-y ------------------ y(y-6)+4(y-6) 6-y ------------------ (y-6)(y-4) now multipling via -a million on dnontr and nmrtr y-6 --------------- (-4-y)(y-6) comparable (y-6) gets canceled, a million ----------- -a million(y+4) thats what i've got been given....