Question

Please hepl with math

Answer 1

`(5^(n+2)-6* 5^(n+1))/(13 *5^(n)-2*5^(n+1)) = -(5)/(3)`

Explanation:

We are given the expression to be simplified:

`(5^(n+2)-6* 5^(n+1))/(13 *5^(n)-2*5^(n+1))`

Let us take common a term with a power of 5 from the numerator and the denominator of the given expression.

We know that:

`a^(p+q) = a^p * a^q`

Let us use it to solve the powers of 5 in the given expression.

`\therefore` we can write:

`5^(n+2) = 5^(n+1)* 5= 5^n* 5^(2)`

`5^(n+1) = 5^n* 5`

The given expression becomes:

`(5^(n+1) * 5-6* 5^(n+1))/(13 *5^(n)-2*5^(n)* 5)`

Taking common
`5^(n+1)` from the numerator and

Taking common
`5^(n)` from the denominator

`\Rightarrow \frac{5^(n+1) (5-6)} {5^(n)(13-2*5)}\\\Rightarrow \frac{5^(n+1) (-1)} {5^(n)(13-10)}\\\Rightarrow -\frac{5^(n+1)} {5^(n)*3}\\\Rightarrow -\frac{5^(n)* 5} {5^(n)*3}\\\Rightarrow -(5)/(3)`

`\therefore` The answer is:

`(5^(n+2)-6* 5^(n+1))/(13 *5^(n)-2*5^(n+1)) = -(5)/(3)`