Solve for $x$ in the expression
$\frac{9x-7}{3x+5}=\frac{3x-4}{x+6}$

Given:

$\frac{9x-7}{3x+5}=\frac{3x-4}{x+6}$

To find Value of $x$

Solution:

By Cross multiplication,

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

=$9 x^{2}  - 7 x + 54 x - 42  =   9 x^{2}  - 12 x + 15 x - 20$

=$9 x^{2}  - 7 x + 54 x - 42  - (  9 x^{2}  - 12 x + 15 x - 20)$ = 0

=$9 x ^{2}  - 7 x + 54 x - 42 - 9 x ^{2}  + 12 x - 15 x + 20 = 0$                          [Since, $9 x ^{2}  -9 x^{2} = 0$]

=$- 7 x + 54 x + 12 x - 15 x - 42 + 20 = 0$

=$47 x - 3 x - 22 = 0$

=$44 x - 22 = 0$

=$44 x = 22$

=>$ x  =  \frac{22 }{44}$

Therefore, $x = \frac{1}{2}$

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Updated on: 10-Oct-2022

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