What is (9.01-9)/(sqrt(9.01)-3) ?

The solution to (9.01-9)/(sqrt(9.01)-3) is (0.01sqrt(901)+0.3)/(0.1)

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simplify (9.01-9)/(sqrt(9.01)-3)

simplify

\frac{9.01 - 9}{9.01 - 3}

\frac{0.01 901 + 0.3}{0.1}

Decimal Notation

6.00166 \dots

Solution steps

\frac{9.01 - 9}{9.01 - 3}

Subtract the numbers:

9.01 - 9 = 0.01

= \frac{0.01}{9.01 - 3}

Multiply by the conjugate

\frac{9.01 + 3}{9.01 + 3}

= \frac{0.01 ( 9.01 + 3 )}{( 9.01 - 3 ) ( 9.01 + 3 )}

Expand

0.01 (9.01 + 3) : \frac{0.01 901 + 0.3}{10}

Expand

(9.01 - 3) (9.01 + 3) : 0.01

= \frac{\frac{0.01 901 + 0.3}{10}}{0.01}

\frac{\frac{0.01 901 + 0.3}{10}}{0.01} = \frac{0.01 901 + 0.3}{0.1}

= \frac{0.01 901 + 0.3}{0.1}

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What is (9.01-9)/(sqrt(9.01)-3) ?
The solution to (9.01-9)/(sqrt(9.01)-3) is (0.01sqrt(901)+0.3)/(0.1)