Solve 3/n^2=n-4/3n^2+2/32n^2

$$\frac{ 3 }{ { n }^{ 2 } } = \frac{ n-4 }{ 3 { n }^{ 2 } } + \frac{ 2 }{ 32 { n }^{ 2 } }$$

Solve for n

$$n = \frac{205}{16} = 12\frac{13}{16} = 12.8125$$

Steps for Solving Linear Equation

Variable n cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 96n^{2}, the least common multiple of n^{2},3n^{2},32n^{2}.

$$96\times 3=32\left(n-4\right)+3\times 2$$

Multiply 96 and 3 to get 288.

$$288=32\left(n-4\right)+3\times 2$$

Use the distributive property to multiply 32 by n-4.

$$288=32n-128+3\times 2$$

Multiply 3 and 2 to get 6.

$$288=32n-128+6$$

Add -128 and 6 to get -122.

$$288=32n-122$$

Swap sides so that all variable terms are on the left hand side.

$$32n-122=288$$

Add 122 to both sides.

$$32n=288+122$$

Add 288 and 122 to get 410.

$$32n=410$$

Divide both sides by 32.

$$n=\frac{410}{32}$$

Reduce the fraction \frac{410}{32} to lowest terms by extracting and canceling out 2.

$$n=\frac{205}{16}$$