What is the limit as x approaches 5 of (1/(9x+9)-1/54)/(1/(9x+10)-1/55) ?

The limit as x approaches 5 of (1/(9x+9)-1/54)/(1/(9x+10)-1/55) is 3025/2916

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limit as x approaches 5 of (1/(9x+9)-1/54)/(1/(9x+10)-1/55)

x \to 5 lim (\frac{\frac{1}{9 x + 9} - \frac{1}{54}}{\frac{1}{9 x + 10} - \frac{1}{55}})

\frac{3025}{2916}

Decimal

1.03737 \dots

Solution steps

x \to 5 lim (\frac{\frac{1}{9 x + 9} - \frac{1}{54}}{\frac{1}{9 x + 10} - \frac{1}{55}})

Simplify

\frac{\frac{1}{9 x + 9} - \frac{1}{54}}{\frac{1}{9 x + 10} - \frac{1}{55}} : \frac{55 ( 9 x + 10 )}{486 ( x + 1 )}

= x \to 5 lim (\frac{55 ( 9 x + 10 )}{486 ( x + 1 )})

Plug in the value

x = 5

= \frac{55 ( 9 \cdot 5 + 10 )}{486 ( 5 + 1 )}

Simplify

\frac{55 ( 9 \cdot 5 + 10 )}{486 ( 5 + 1 )} : \frac{3025}{2916}

= \frac{3025}{2916}

What is the limit as x approaches 5 of (1/(9x+9)-1/54)/(1/(9x+10)-1/55) ?
The limit as x approaches 5 of (1/(9x+9)-1/54)/(1/(9x+10)-1/55) is 3025/2916