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To start, let `y = log x` .
To eliminate the denominators, multiply both sides by the LCD which is `12(7-y)(11+y)` .
Then, express the equation in quadratic form `ax^2+bx+c=0` .
Then, factor left side.
Set each factor to zero and solve for y.
`13y-19=0` and `y-1=0`
To solve for x, substitute the value of y to `y = logx` . Then, express it to its equivalent exponential form which is `10^y=x` .
`y=19/13` , `19/13=log x`
`y=1` , `1 = log x`
`x = 10`
Hence, the solutions are `x=10` and `x=10^(19/13)` .
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