Solve 1/11-n-2(3n-1)/-7n^2+74n+33=1/7n+3

$$\frac { 1 } { 11 - n } - \frac { 2 ( 3 n - 1 ) } { - 7 n ^ { 2 } + 74 n + 33 } = \frac { 1 } { 7 n + 3 }$$

Solve for n

$$n=3$$

Steps for Solving Linear Equation

Variable n cannot be equal to any of the values -\frac{3}{7},11 since division by zero is not defined. Multiply both sides of the equation by \left(n-11\right)\left(7n+3\right), the least common multiple of 11-n,-7n^{2}+74n+33,7n+3.

$$-3-7n+2\left(3n-1\right)=n-11$$

Use the distributive property to multiply 2 by 3n-1.

$$-3-7n+6n-2=n-11$$

Combine -7n and 6n to get -n.

$$-3-n-2=n-11$$

Subtract 2 from -3 to get -5.

$$-5-n=n-11$$

Subtract n from both sides.

$$-5-n-n=-11$$

Combine -n and -n to get -2n.

$$-5-2n=-11$$

Add 5 to both sides.

$$-2n=-11+5$$

Add -11 and 5 to get -6.

$$-2n=-6$$

Divide both sides by -2.

$$n=\frac{-6}{-2}$$

Divide -6 by -2 to get 3.

$$n=3$$