I just need help getting x on top. May you assist me?

Question

24, 27 and 30 I need to solve for x. The x is on th bottom of the fraction and all i need is to get the x on top and then I can solve it myself. Thanks for helping!

24. 1/x-2 + 3/x+3 = 4/x(squared)+x-6

27. 1/x + 2/x-5 = 0

30. 3= 2 + 2/z+2

Answer 1

in all of your answers all you need to do is multiply the whole fraction by the inverse of the denominator 27 would be: [1(1/x)/(x)(1/x)] + [2(1/x)/(x)(1/x)]=5

So the denominator becomes x/x which equals 1

So on and so forth with the rest of them

Answer 2

1/x-2 + 3/x+3 = 4/x^2+x-6

* notice that multiplying (x-2) and (x+3) will yield x^2+x-6

just multiply both sides by x^2+x-6 to transfer x to the numerator

--- (1/x-2) X (x^2+x-6)  +  (3/x+3) X (x^2+x-6) = (4/x^2+x-6) X (x^2+x-6)

* that'll give you

1 X (x+3)  +  3 ( x-2)  = 4

27. 1/x + 2/x-5 = 0

*again, multiply both sides of the equation by the LCM of the denominators which in

this case is: (x)(x-5)

= (x)(x-5) X [1/x + 2/x-5 = 0]

= 1 (x-5) + 2(x)=0

30. 3= 2 + 2/z+2

multiply both sides by the LCM of the denominators. it's just z there so

the LCM is z

[3= 2 + 2/z+2] X z

3z= 2z + 2 +2z