What is (x^3+1)/(x^2(x+1)-x(x+1)+(x+1)) ?

The solution to (x^3+1)/(x^2(x+1)-x(x+1)+(x+1)) is 1

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simplify (x^3+1)/(x^2(x+1)-x(x+1)+(x+1))

simplify

\frac{x ^{3} + 1}{x ^{2} ( x + 1 ) - x ( x + 1 ) + ( x + 1 )}

1

Solution steps

\frac{x ^{3} + 1}{x ^{2} ( x + 1 ) - x ( x + 1 ) + ( x + 1 )}

Apply rule:

a + (b + c) = a + b + c

- x (x + 1) + (x + 1) = - x (x + 1) + x + 1

= \frac{x ^{3} + 1}{x ^{2} ( x + 1 ) - x ( x + 1 ) + x + 1}

Factor

x^{3} + 1 : (x + 1) (x^{2} - x + 1)

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

Factor out common term

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

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

Apply the fraction rule:

\frac{a}{a} = 1

= 1

(x^{2} + 7)^{2} + 7

- (- 6)^{2}

\frac{4}{5} \div \frac{3}{7}

m \cdot m

(- 3)^{\frac{1}{2}}

What is (x^3+1)/(x^2(x+1)-x(x+1)+(x+1)) ?
The solution to (x^3+1)/(x^2(x+1)-x(x+1)+(x+1)) is 1