Question

Solve the equation :9x+7/3x+5=3x-4/x+6​

Answer 1

We have, (9x-7)/(3x+5) = (3x-4)/(x+6)

(9x-7)/(3x+5) – (3x-4)/(x+6) = 0

 LCM = (3x+5) (x+6) ((9x-7) (x+6) – (3x-4) (3x+5)) / (3x+5) (x+6) = 0

cross-multiplying the both,  (9x-7) (x+6) – (3x-4) (3x+5) = 0

expanding the above eqn we get, 9x2 + 54x – 7x – 42 – (9x2 + 15x – 12x – 20) = 0

44x – 22 = 0

44x = 22 x

= 22/44 =

2/4 =

1/2

verification

(9x-7)/(3x+5) = (3x-4)/(x+6)

put x = 1/2

(9(1/2) – 7) / (3(1/2) + 5) = (3(1/2) – 4) / ((1/2) + 6)

(9/2 – 7) / (3/2 + 5) = (3/2 – 4) / (1/2 + 6)

((9-14)/2) / ((3+10)/2) = ((3-8)/2) / ((1+12)/2)

-5/2 / 13/2 =

-5/2 / 13/2

-5/13 = -5/13

hence proved