What is expand (αβ)/((α+β)^2(α+β+1)) ?

The solution to expand (αβ)/((α+β)^2(α+β+1)) is (αβ)/(α^3+3α^2β+α^2+3αβ^2+2αβ+β^3+β^2)

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expand (αβ)/((α+β)^2(α+β+1))

expand

\frac{α β}{( α + β ) ^{2} ( α + β + 1 )}

\frac{α β}{α ^{3} + 3 α ^{2} β + α ^{2} + 3 α β ^{2} + 2 α β + β ^{3} + β ^{2}}

Solution steps

\frac{α β}{( α + β ) ^{2} ( α + β + 1 )}

(α + β)^{2} = α^{2} + 2 α β + β^{2}

= \frac{α β}{( α ^{2} + 2 α β + β ^{2} ) ( α + β + 1 )}

Expand

(α^{2} + 2 α β + β^{2}) (α + β + 1) : α^{3} + 3 α^{2} β + α^{2} + 3 α β^{2} + 2 α β + β^{3} + β^{2}

= \frac{α β}{α ^{3} + 3 α ^{2} β + α ^{2} + 3 α β ^{2} + 2 α β + β ^{3} + β ^{2}}

(\frac{x}{x + 1})^{2}

- \frac{3}{3 ( x + h ) + 4}

3 x (\frac{1}{x})

(x + 3) (x + 1) (3 x +!)

- 3 (1 - 7 n = 9) (- 6 + 8 n)

What is expand (αβ)/((α+β)^2(α+β+1)) ?
The solution to expand (αβ)/((α+β)^2(α+β+1)) is (αβ)/(α^3+3α^2β+α^2+3αβ^2+2αβ+β^3+β^2)