Solve 1/(n-2)-1/2=2/15

$$\frac { 1 } { ( n - 2 ) } - \frac { 1 } { 2 } = \frac { 2 } { 15 }$$

Solve for n

$$n = \frac{68}{19} = 3\frac{11}{19} \approx 3.578947368$$

Steps for Solving Linear Equation

Variable n cannot be equal to 2 since division by zero is not defined. Multiply both sides of the equation by 30\left(n-2\right), the least common multiple of n-2,2,15.

$$30+30\left(n-2\right)\left(-\frac{1}{2}\right)=4\left(n-2\right)$$

Multiply 30 and -\frac{1}{2} to get -15.

$$30-15\left(n-2\right)=4\left(n-2\right)$$

Use the distributive property to multiply -15 by n-2.

$$30-15n+30=4\left(n-2\right)$$

Add 30 and 30 to get 60.

$$60-15n=4\left(n-2\right)$$

Use the distributive property to multiply 4 by n-2.

$$60-15n=4n-8$$

Subtract 4n from both sides.

$$60-15n-4n=-8$$

Combine -15n and -4n to get -19n.

$$60-19n=-8$$

Subtract 60 from both sides.

$$-19n=-8-60$$

Subtract 60 from -8 to get -68.

$$-19n=-68$$

Divide both sides by -19.

$$n=\frac{-68}{-19}$$

Fraction \frac{-68}{-19} can be simplified to \frac{68}{19} by removing the negative sign from both the numerator and the denominator.

$$n=\frac{68}{19}$$