What is n(1-t/(1-x))^{n-1}*1/(1-x) ?

The solution to n(1-t/(1-x))^{n-1}*1/(1-x) is (n(1-x-t)^{n-1})/((1-x)^n)

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simplify n(1-t/(1-x))^{n-1}*1/(1-x)

simplify

n (1 - \frac{t}{1 - x})^{n - 1} \cdot \frac{1}{1 - x}

\frac{n ( 1 - x - t ) ^{n - 1}}{( 1 - x ) ^{n}}

Solution steps

n (1 - \frac{t}{1 - x})^{n - 1} \frac{1}{1 - x}

Simplify

(1 - \frac{t}{1 - x})^{n - 1} : \frac{( 1 - x - t ) ^{n - 1}}{( 1 - x ) ^{n - 1}}

= n \frac{( 1 - x - t ) ^{n - 1}}{( 1 - x ) ^{n - 1}} \cdot \frac{1}{1 - x}

Apply the fraction rule:

a \cdot \frac{b}{c} \cdot \frac{d}{e} = \frac{a \cdot b \cdot d}{c \cdot e}

= \frac{n ( 1 - x - t ) ^{n - 1} \cdot 1}{( 1 - x ) ^{n - 1} ( 1 - x )}

Apply rule:

a \cdot 1 = a

n (1 - x - t)^{n - 1} \cdot 1 = n (1 - x - t)^{n - 1}

= \frac{n ( 1 - x - t ) ^{n - 1}}{( 1 - x ) ^{n - 1} ( 1 - x )}

Simplify

(1 - x)^{n - 1} (1 - x) : (1 - x)^{n}

= \frac{n ( 1 - x - t ) ^{n - 1}}{( 1 - x ) ^{n}}

2 x^{2} + 6 x + 8 = 0

(1 + 2) (1 - 2)

x^{2} + 10 x + 25 < 0

15 = 3 \cdot \frac{1}{2} s

2 x^{3} - 16 x^{2} + 30 x

What is n(1-t/(1-x))^{n-1}*1/(1-x) ?
The solution to n(1-t/(1-x))^{n-1}*1/(1-x) is (n(1-x-t)^{n-1})/((1-x)^n)