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

Step 1: Multiply everything by x-4 to give 

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

Step2: Multiply everything by 2x+1 to give

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

Step 3: Multiply out the brackets to give

(4x2+8x+3)-(2x2-16x+32)=2x2-7x-4

Step 4: Simplify to get a zero on one side of the equation to give

31x-25=0

Step 5: We therefore know that 31x = 25 so to find x divide 25 by 31 to get x=0.81 to 2 decimal places

Matthew T. A Level Maths tutor, GCSE Maths tutor, GCSE Physics tutor,...

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