Show that (4x-5)/(2x+1) =2-((7)/(2x+1))?

Method 1 :

L.H.S.
= (4x - 5) / (2x + 1)
= [(4x + 2) - 7] / (2x + 1)
= [2(2x + 1) - 7] / (2x + 1)
= [2(2x + 1) / (2x + 1)] - [7 / (x + 1)]
= 2 - [7 / (2x + 1)]
= R.H.S.

Hence, (4x - 5) / (2x + 1) = 2 - [7 / (2x + 1)]


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Method 2 :

R.H.S.
= 2 - [7 / (2x + 1)]
= [2(2x + 1) / (2x + 1)] - [7 / (x + 1)]
= [2(2x + 1) - 7] / (2x + 1)
= [4x + 2 - 7] / (2x + 1)
= (4x - 5) / (2x + 1)
= L.H.S.

Hence, (4x - 5) / (2x + 1) = 2 - [7 / (2x + 1)]

On the right side of the equation, it can be rewritten as 2/(1) -7/(2x+1). Now, we cannot subtract this without a common denominator. So, 2(2x+1)/1(2x+1)-7(1)/(2x+1)(1) which gives you (4x+2/2x+1)-7/2x+1. Now, you can combine like terms +2-7 equals -5. Hence, 4x-5/2x+1.