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erastova [34]
3 years ago
11

Express in Simper Fom : y-x

Mathematics
1 answer:
AveGali [126]3 years ago
6 0
Simplify

E=\dfrac{\frac{x}{y}-\frac{y}{x}}{\frac{1}{y}+\frac{1}{x}}


Conditions for the existance of E:

x\neq 0~~\text{ and}~~y\neq 0~~\text{ and }~~x\neq -y.

(otherwise, the one of the denominators would be zero.)
____________________

Simplifying:

E=\dfrac{\frac{x}{y}-\frac{y}{x}}{\frac{1}{y}+\frac{1}{x}}


Multiply both the numerator and the denominator by xy:

E=\dfrac{xy\cdot \left(\frac{x}{y}-\frac{y}{x} \right )}{xy\cdot \left(\frac{1}{y}+\frac{1}{x} \right )}\\\\\\ E=\dfrac{\frac{xy\cdot x}{y}-\frac{xy\cdot y}{x}}{\frac{xy}{y}+\frac{xy}{x}}\\\\\\ E=\dfrac{x^{2}-y^{2}}{x+y}\\\\\\ E=\dfrac{(x+y)(x-y)}{x+y}


Simplify common factors:

E=x-y\\\\\\ \therefore~~\boxed{\begin{array}{c}\dfrac{\frac{x}{y}-\frac{y}{x}}{\frac{1}{y}+\frac{1}{x}}=x-y \end{array}}

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