What is expand (k(4k+5)+1)/((4k+1)(4k+5)) ?

The solution to expand (k(4k+5)+1)/((4k+1)(4k+5)) is (k+1)/(4k+5)

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expand (k(4k+5)+1)/((4k+1)(4k+5))

expand

\frac{k ( 4 k + 5 ) + 1}{( 4 k + 1 ) ( 4 k + 5 )}

\frac{k + 1}{4 k + 5}

Solution steps

\frac{k ( 4 k + 5 ) + 1}{( 4 k + 1 ) ( 4 k + 5 )}

Expand

(4 k + 1) (4 k + 5) : 16 k^{2} + 24 k + 5

= \frac{k ( 4 k + 5 ) + 1}{16 k ^{2} + 24 k + 5}

Expand

k (4 k + 5) + 1 : 4 k^{2} + 5 k + 1

= \frac{4 k ^{2} + 5 k + 1}{16 k ^{2} + 24 k + 5}

Factor

4 k^{2} + 5 k + 1 : (4 k + 1) (k + 1)

= \frac{( 4 k + 1 ) ( k + 1 )}{16 k ^{2} + 24 k + 5}

Factor

16 k^{2} + 24 k + 5 : (4 k + 1) (4 k + 5)

= \frac{( 4 k + 1 ) ( k + 1 )}{( 4 k + 1 ) ( 4 k + 5 )}

Cancel the common factor:

4 k + 1

= \frac{k + 1}{4 k + 5}

\frac{4}{5} (20 x - 10)

(3 x - 4 y = 4,) (5 x - 2 y = 9)

e^{x} \cdot (x + y)

(y^{3} + 10 x y^{4} - 2 x) d x

e^{4 (l n ∣ x ∣ + C)}

What is expand (k(4k+5)+1)/((4k+1)(4k+5)) ?
The solution to expand (k(4k+5)+1)/((4k+1)(4k+5)) is (k+1)/(4k+5)