What is (x^{-1}+1)/(yx^{-1)+x} ?

The solution to (x^{-1}+1)/(yx^{-1)+x} is (x+1)/(x^2+y)

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simplify (x^{-1}+1)/(yx^{-1)+x}

simplify

\frac{x ^{- 1} + 1}{y x ^{- 1} + x}

\frac{x + 1}{x ^{2} + y}

Solution steps

\frac{x ^{- 1} + 1}{y x ^{- 1} + x}

Simplify

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

= \frac{\frac{x + 1}{x}}{y x ^{- 1} + x}

Simplify

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

= \frac{\frac{x + 1}{x}}{\frac{x ^{2} + y}{x}}

Apply the fraction rule:

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

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

Cancel the common factor:

x

= \frac{x + 1}{x ^{2} + y}

\frac{3 x ^{3}}{6 y ^{2}} \cdot \frac{4 y ^{5}}{7 x ^{4}}

∣ y ∣ - 3 \leq 0

(y^{2})^{4}

\frac{x - 3}{x + 1} < 1

r^{2} + 3 r - 1 = 0

What is (x^{-1}+1)/(yx^{-1)+x} ?
The solution to (x^{-1}+1)/(yx^{-1)+x} is (x+1)/(x^2+y)