x+1/x-1=3x-7/2x-5

Asked by pruthaveshmenesj01052 | 6th Jun, 2021, 09:42: PM

Expert Answer:

begin mathsize 14px style fraction numerator x plus 1 over denominator x minus 1 end fraction space equals space fraction numerator 3 x minus 7 over denominator 2 x minus 5 end fraction end style
 
After cross multiplying , we get
 
( x + 1 ) ( 2x - 5 ) = ( 3x -7 ) ( x - 1 ) 
 
2x2 -3x -5 = 3x2 - 10x  + 7
 
X2 - 7x + 12 = 0
 
(x-4) ( x-3 ) = 0
 
x = 4 or x = 3
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Alternate method by ratio and proportion
 
begin mathsize 14px style fraction numerator x plus 1 over denominator x minus 1 end fraction space equals space fraction numerator 3 x minus 7 over denominator 2 x minus 5 end fraction end style  .............................(1)
 
If (a/b) = (c/d ) , then we have  ( a + b ) / (a - b )  = ( c + d ) / ( c - d )  .........................(2)
 
Using above property of ratio and proportion, given eqn.(1) is written as
 
( x / 1 )   = [ ( 3x - 7 ) + ( 2x - 5 ) ] / [ (3x-7 ) - (2x -5 ) ] 
 
x = ( 5x - 12 ) / ( x -2 )
 
x2 - 2x = 5x - 12 
 
x2 - 7x +12 = 0  or  ( x-4) ( x- 3 ) = 0
 
Hence , we get , x = 3 or x = 4 
 
 

Answered by Thiyagarajan K | 20th Sep, 2021, 12:34: PM