If (2x+3)/(x-4)-(2x-8)/(2x+1)=1, what is x?

First eliminate fractions;

    Multiplying both sides by (x-4) gives;

    (2x+3)-((2x-8)(x-4))/(2x+1)=(x-4)

    Multiplying both sides by (2x+1) gives;

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

Now simplify the expression;

    Expanding the brackets gives;

    (4x2+2x+6x+3)-(2x2-8x-8x+32)=(2x2+x-8x-4)

    2x2+24x-29=2x2-7x-4

    Subtract (2x2-7x-4) from both sides;

    31x-25=0

Rearrange for x;

31x=25

x=25/31

HC
Answered by Hannah C. Maths tutor

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