What is factor 4(x-5)^{-9}+3(x-5)^{-8} ?

The solution to factor 4(x-5)^{-9}+3(x-5)^{-8} is (3x-11)/((-5+x)^9)

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factor 4(x-5)^{-9}+3(x-5)^{-8}

factor

4 (x - 5)^{- 9} + 3 (x - 5)^{- 8}

\frac{3 x - 11}{( - 5 + x ) ^{9}}

Solution steps

4 (x - 5)^{- 9} + 3 (x - 5)^{- 8}

Apply exponent rule:

a^{b + c} = a^{b} a^{c}

(- 5 + x)^{- 8} = (- 5 + x)^{- 9} (- 5 + x)

= 4 (- 5 + x)^{- 9} + 3 (- 5 + x)^{- 9} (- 5 + x)

Factor out common term

(- 5 + x)^{- 9}

= (- 5 + x)^{- 9} (4 + 3 (- 5 + x))

Expand

3 (x - 5) + 4 : 3 x - 11

= (x - 5)^{- 9} (3 x - 11)

Refine

= \frac{3 x - 11}{( x - 5 ) ^{9}}

[- 1.9]

a y - 2 b y + 2 a x - 4 b x

6 x^{2} - (- 2) x + 9 x - 3

C_{1} e^{x} + C_{2} e^{- x}

25 + (tan (5 x))^{2}

What is factor 4(x-5)^{-9}+3(x-5)^{-8} ?
The solution to factor 4(x-5)^{-9}+3(x-5)^{-8} is (3x-11)/((-5+x)^9)