Question

((2 x + 5)/(x- 5))- 2((x- 5)/(2x+ 5) is equal to(-17 / 28).Solve for x.

Answer 1

hope this helps you

after equation you can solve it

Answer 2

((2 x + 5)/(x- 5))- 2((x- 5)/(2x+ 5) is equal to(-17 / 28)

Let (2x+5)/(x-5) = a ---( 1 )

Now , Rewrite the problem,

a - 2/a = -17/28

=> (a²-2)/a = -17/28

=> 28(a²-2)= -17a

=> 28a² - 56 +17a = 0

=> 28a²+17a-56 = 0

Splitting the middle term,we

get

=> 28a²+49a-32a-56=0

=> 7a(4a+7)-8(4a+7)=0

=> (4a+7)(7a-8)=0

=> 4a+7 = 0 or 7a-8 = 0

i ) 4a+7=0

=> 4[(2x+5)/(x-5)]+7 = 0

=> 4(2x+5)+7(x-5)=0

=> 8x+20+7x-35=0

=> 15x-15=0

=> 15x = 15

=> x = 15/15 = 1

ii ) 7a-8=0

=> 7[(2x+5)/(x-5)] -8 = 0

=> 7(2x+5)-8(x-5)=0

=> 14x+35-8x+40=0

=> 6x+75=0

=> x = -75/6

=> x = - 25/2

Therefore ,

x=1 or x = -25/2

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