# GCSE Maths - Solve the equation (2x+3)/(x-4) - (2x-8)/(2x+1) = 1 Give your answer to 2 decimal places.

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This is an A* level GCSE Maths question. 'Solve' means we need to find what value x represents, but in the question this x appears on the denominator (bottom half) of the fractions which we can't use. So the first thing we have to do is multiply out by the denominators to get rid of them. Lets do this one by one.

So first if we multiply through every term by (x-4) we'll be left with:

(2x+3) - (2x-8)(x-4)/(2x+1) = 1(x-4)

Now lets multiply through every term by (2x+1) which will eliminate the remaining fraction:

(2x+3)(2x+1) - (2x-8)(x-4) = 1(x-4)(2x+1)

Now expand out the brackets (be careful theres going to be a lot of terms) but you should get:

(4x^2+2x+6x+3) - (2x^2-8x-8x+32) = (2x^2-8x-4)

and now simplify \9being careful with the negatives) to:

2x^2+24x-29 = 2x^2-7x-4

subtract the 2x^2 from both sides, and collect like terms (so all x's on one side of the equation, and numbers on the other) do this by moving the 7x to the left hand side (+7x to both sides) and 29 to the right hand side (+29 to both sides) this will give you:

31x=25

divide both sides by 31:

x=25/31

x=0.8064516129

But remember the question asked for the answer to be given to 2 decimal places so:

x=0.81 (2 d.p.)

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