What is (x-2/(x+1))(x+1/(x+2)) ?

The solution to (x-2/(x+1))(x+1/(x+2)) is (x-1)(x+1)

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simplify (x-2/(x+1))(x+1/(x+2))

simplify

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

(x - 1) (x + 1)

Solution steps

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

Join

x - \frac{2}{x + 1} : \frac{x ^{2} + x - 2}{x + 1}

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

Apply the fraction rule:

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

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

Simplify

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

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

Factor

x^{2} + 2 x + 1 : (x + 1)^{2}

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

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

(x + 1)^{2} = (x + 1) (x + 1)

= \frac{( x - 1 ) ( x + 1 ) ( x + 1 )}{x + 1}

Cancel the common factor:

x + 1

= (x - 1) (x + 1)

(x - 1)^{3}

(4 x - 5 i)^{2}

\frac{\partial}{\partial x} ((y) (x^{2} + y^{2}))

\frac{a - bi}{1 + ( a + bi ) ^{2}}

(a^{2} - \frac{1}{a})^{4}

What is (x-2/(x+1))(x+1/(x+2)) ?
The solution to (x-2/(x+1))(x+1/(x+2)) is (x-1)(x+1)