Question #d9f0b

2 Answers
Sahar Mulla ❤
Feb 4, 2018

#2/(2x+11)-1/(x-4)=1/2#

#(2(x-4) - 1(2x+11))/((2x+11)(x-4) )=1/2#

#(2x-8-2x-11)/(2x^2+11x-8x-44) = 1/2#

#(-19)/(2x^2+3x-44) = 1/2#

#-38=2x^2+3x-44#

#=2x^2+3x+38-44#

#=2x^2+3x-6#

EZ as pi
Feb 4, 2018

Get rid of the denominators by multiplying through by the LCM.

Move all the terms to one side and simplify.

Explanation:

You need to get rid of the denominators in the given equation.
You can do this by multiplying each term by the LCM of the denominators, which is #color(blue)(2(2x+11)(x-4))#..

Each denominator will cancel.

The left side will look like this:

#(2xxcolor(blue)(2cancel((2x+11))(x-4)))/cancel((2x+11)) -(1xxcolor(blue)(2(2x+11)cancel((x-4))))/cancel((x-4))#

and the right side like this: #(1xxcolor(blue)(cancel2(2x+11)(x-4)))/cancel2#

This leaves the equation without fractions.

#4(x-4) -2(2x+11) = (2x+11)(x-4)#

Multiply out the brackets:

#4x-16 -4x-22 = 2x^2 +3x-44#

Move all the terms to the right hand side.

#0 = 2x^2 +3x -44+38#

#0 = 2x^2 +3x -6#

This is the required equation.

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