Math Olympiad | A Nice Rational Equation | 80% Failed to solve!

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[@RyanLewis-Johnson-wq6xs]

It’s in my head.

[@RyanLewis-Johnson-wq6xs]

(3x-5)/(5x-5)+(5x-1)/(7x-7)-(x-4)/(1-x)=2 x=10

[@uttiyamajumdar8928]

(3x-5)/(5x-5)+(5x-1)/(7x-7)-(x-4)/(1-x)=2 ⇒1/5 (3x-5)+1/7 (5x-1)+(x-4)=2(x-1) ⇒3/5 x+5/7 x+x-5/5-1/7-4=2x-2 ⇒3/5 x+5/7 x+x-2x=5/5+1/7+4-2 ⇒(3/5+5/7-1)x=3+1/7 ⇒((21+25)/35-1)x=22/7 ⇒10/35 x=22/7 ⇒2x=22⇒x=11

[@Danieswors]

10

[@ganeshdas3174]

x = 10