What is 4/(n-4)-(2-n)/n ?

The solution to 4/(n-4)-(2-n)/n is (n^2-2n+8)/(n(n-4))

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simplify 4/(n-4)-(2-n)/n

simplify

\frac{4}{n - 4} - \frac{2 - n}{n}

\frac{n ^{2} - 2 n + 8}{n ( n - 4 )}

Solution steps

\frac{4}{n - 4} - \frac{2 - n}{n}

Least Common Multiplier of

n - 4, n : n (n - 4)

Adjust Fractions based on the LCM

= \frac{4 n}{n ( n - 4 )} - \frac{( 2 - n ) ( n - 4 )}{n ( n - 4 )}

Apply the fraction rule:

\frac{a}{c} - \frac{b}{c} = \frac{a - b}{c}

= \frac{4 n - ( 2 - n ) ( n - 4 )}{n ( n - 4 )}

Simplify

4 n - (2 - n) (n - 4) : n^{2} - 2 n + 8

= \frac{n ^{2} - 2 n + 8}{n ( n - 4 )}

64 \cdot \frac{1}{4}

2 (10 - 6 x) = x - 8 x

∣ 3 x - 2 ∣ + 16 < 7

x^{2} - 10 x - 3 = 0

What is 4/(n-4)-(2-n)/n ?
The solution to 4/(n-4)-(2-n)/n is (n^2-2n+8)/(n(n-4))