Question #cf38f

2 Answers
P dilip_k
Mar 17, 2017

#(x-1)/(x-2) -(x-5)/(x-6)=(x-3)/(x-4)-(x-7)/(x-8)#

#=>(x-2+1)/(x-2) -(x-6+1)/(x-6)=(x-4+1)/(x-4)-(x-8+1)/(x-8)#

#=>1+1/(x-2) -1-1/(x-6)=1+1/(x-4)-1-1/(x-8)#

#=>1/(x-2) -1/(x-6)=1/(x-4)-1/(x-8)#

#=>(x-6-x+2)/((x-2)(x-6))=(x-8-x+4)/((x-4)(x-8))#

#=>-4/((x-2)(x-6))=-4/((x-4)(x-8))#

#=>(x-2)(x-6)=(x-4)(x-8)#

#=>x^2-8x+12=x^2-12x+32#

#=>12x-8x=32-12=20#

#=>4x=20#

#=>x=20/4=5#

t0hierry · Ratnaker Mehta
Mar 17, 2017

#(x-1)/(x-2) - (x-5)/(x-6) = [(x-1)(x-6)-(x-2)(x-5)] /[(x-2)(x-6)] = (x^2 -6x -x + 6 - x^2 + 5x + 2x - 10)/[(x-2)(x-6)] =-4/[(x-2)(x-6)]#

Explanation:

#(x-1)/(x-2) - (x-5)/(x-6) = [(x-1)(x-6)-(x-2)(x-5)] /[(x-2)(x-6)]= (x^2 -6x -x + 6 - x^2 + 5x + 2x - 10)/[(x-2)(x-6)] =-4/[(x-2)(x-6)]#
#(x-3)/(x-4) - (x-7)/(x-8) = [(x-3)(x-8)-(x-4)(x-7)] /[(x-4)(x-8)]= (x^2 -8x -3x + 24 - x^2 + 7x + 4x - 28)/[(x-4)(x-8)] =-4/[(x-4)(x-8)]#
So you get
#(x-2)(x-6) = (x-4)(x-8)#
# 4x=20.#
#x = 5.#

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