What is 1/(1+(y/x)^2)*1/x ?

The solution to 1/(1+(y/x)^2)*1/x is x/(x^2+y^2)

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simplify 1/(1+(y/x)^2)*1/x

simplify

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

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

Solution steps

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

Simplify

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

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

Apply the fraction rule:

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

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

Apply rule:

a \cdot 1 = a

x^{2} \cdot 1 = x^{2}

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

Apply exponent rule:

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

x^{2} = xx

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

Cancel the common factor:

x

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

\frac{4 j k ^{2} - 2 j ^{3} k ^{4}}{2 jk}

10 x^{2} - 9 x - 9 = 0

x^{2} - 5 x - 24 = 0

4 (8 - 2 x) + 2 x < 5 (9 + 3 x)

4 (2 y + 5) < 3 (5 y - 2)