Question

Do I need common denominators? Where do I start? Please just show me how to work these, I have a test soon and I really need to grasp this better. (I know I've been asking a few questions, sorry! English is my better subject... not math haha)

Solve.

1. (18)/(x-2) = 1 + (20)/(x+2)


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

Answer 1

1) in the RHS first get a common denominotor then cross multiply LHS and RHS and solve the eq.

Answer 2

there is a pic to better show problems

Answer 3

The first thing you have to realize is that no denominator can equal 0 in the equation, do you know why?

Answer 4

1) in rhs
1 + 20/x+2
now make the denominator common for the 2 terms i.e. (x+2)+20/(x+2)

now cross multiply lhs and rhs

Answer 5

koel do you mind writing it out so i can see the steps?

Answer 6

i think i know what you're saying but not 100% sure

Answer 7

7) remove the denominators:

multiply both sides by (2x + 1) and (x + 4)

2x+1 is removed from the LHS, (x+4) is removed in RHS
then solve.

Answer 8

\[\large \frac{18}{x-2}=1+\frac{20}{x+2}\]
Multiply both sides by (x-2)
\[\large 18=(x-2)[1+\frac{20}{x+2}]\]
\[\large 18=(x-2)+\frac{20(x-2)}{x+2}\]
\[\large 18=\frac{(x-2)(x+2)+20x-40}{x+2}\]
\[\large 18=\frac{x^2-4+20x-40}{x+2}\]
\[\large 18=\frac{x^2+20x-44}{x+2}\]
Multiply both sides by x+2
\[\large 18(x+2)=x^2+20x-44\]
\[\large 18x+36=x^2+20x-44\]
Move everything to RHS (Right Hand Side) and collect like terms
\[\large x^2+2x-100=0\]

Answer 9

Use the quadratic formula to find your x-values. Make sure you do not include x=-2 and x+2 as your answers. They cannot be included since the denominator of the fractions in your original equation cannot equal to zero.

Answer 10

x=-2 and x=+2*

Answer 11

\[(18/x-2) =1 +(20/x+2)\]
\[(18/x-2) =(x+2 +20)/(x+2)\]
\[18/x-2 = x+22/x+2\]
18(x+2) = (x-2)(x+22)
18x+36 = x2 -2x +22x -44
2x = 80
x=40

Answer 12

similarly try doing the 2nd ques

Answer 13

okay thanks everyone!! :) Helped a lot!!!