What is the domain of f(x)=((x5^x))/(5^{(x+2))-5} ?

The domain of f(x)=((x5^x))/(5^{(x+2))-5} is x -1

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domain of f(x)=((x5^x))/(5^{(x+2))-5}

domain

f (x) = \frac{( x 5 ^{x} )}{5 ^{(x + 2)} - 5}

x < - 1 or x > - 1

Interval Notation

(- \infty, - 1) \cup (- 1, \infty)

Solution steps

Find undefined (singularity) points:

x = - 1

The function domain

x < - 1 or x > - 1

f (x) = \frac{7 x}{x ^{2} - 3 x + 2}

f (x) = \frac{( x 5 ^{x} )}{5 ^{(x + 2)} - 4}

5 x + 6 - 1 - 8 x

x^{4} + 2 x^{3} + 2 x^{2} + x

f (x) = \frac{( x - 2 ) + ( x - 1 )}{( x - 2 ) + x - 1}

What is the domain of f(x)=((x5^x))/(5^{(x+2))-5} ?
The domain of f(x)=((x5^x))/(5^{(x+2))-5} is x<-1\lor x>-1