What is (\frac{(k-4)(2k+1))/(5(2k+1))}{((k-3)(k-4))/(10(k-3))} ?

The solution to (\frac{(k-4)(2k+1))/(5(2k+1))}{((k-3)(k-4))/(10(k-3))} is 2

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simplify (\frac{(k-4)(2k+1))/(5(2k+1))}{((k-3)(k-4))/(10(k-3))}

simplify

\frac{\frac{( k - 4 ) ( 2 k + 1 )}{5 ( 2 k + 1 )}}{\frac{( k - 3 ) ( k - 4 )}{10 ( k - 3 )}}

2

Solution steps

\frac{\frac{( k - 4 ) ( 2 k + 1 )}{5 ( 2 k + 1 )}}{\frac{( k - 3 ) ( k - 4 )}{10 ( k - 3 )}}

Apply the fraction rule:

\frac{\frac{a}{b}}{\frac{c}{d}} = \frac{a \cdot d}{b \cdot c}

= \frac{( k - 4 ) ( 2 k + 1 ) \cdot 10 ( k - 3 )}{5 ( 2 k + 1 ) ( k - 3 ) ( k - 4 )}

Cancel the common factor:

k - 4

= \frac{( 2 k + 1 ) \cdot 10 ( k - 3 )}{5 ( 2 k + 1 ) ( k - 3 )}

Cancel the common factor:

2 k + 1

= \frac{10 ( k - 3 )}{5 ( k - 3 )}

Cancel the common factor:

k - 3

= \frac{10}{5}

Divide the numbers:

\frac{10}{5} = 2

= 2

10935

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What is (\frac{(k-4)(2k+1))/(5(2k+1))}{((k-3)(k-4))/(10(k-3))} ?
The solution to (\frac{(k-4)(2k+1))/(5(2k+1))}{((k-3)(k-4))/(10(k-3))} is 2