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

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

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

simplify

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

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

Solution steps

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

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

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

Apply exponent rule:

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

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

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

Cancel the common factor:

1 + sin (x)

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

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

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

\frac{5}{3} \times \frac{6}{2}

18.5

4 y^{6} - 121

2 \frac{1}{4} \times 3

\frac{4 - 1}{2}

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