Question

(x/y^2-1/x):(1/y-1/x )

Answer 1

Ответ:

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Объяснение:

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Answer 2

To simplify the expression $\frac{\frac{x}{y^2} - \frac{1}{x}}{\frac{1}{y} - \frac{1}{x}}$, you can start by finding a common denominator for the fractions in the numerator and denominator.

First, let's find a common denominator for the fractions in the numerator:

1. The first fraction is $\frac{x}{y^2}$. To have a common denominator with the second fraction, we can express it with a denominator of $x$. So, we multiply both the numerator and denominator of the first fraction by $x$, which gives us $\frac{x^2}{xy^2}$.

2. The second fraction is $\frac{1}{x}$, which already has a denominator of $x$.

Now, let's find a common denominator for the fractions in the denominator:

1. The first fraction is $\frac{1}{y}$, which already has a denominator of $y$.

2. The second fraction is $\frac{1}{x}$, which already has a denominator of $x$.

Now that we have a common denominator, we can rewrite the expression as follows:

$\frac{\frac{x^2}{xy^2} - \frac{1}{x}}{\frac{1}{y} - \frac{1}{x}}$

Next, we can simplify the expression further by combining the fractions in the numerator and denominator:

Numerator: $\frac{x^2}{xy^2} - \frac{1}{x}$

Denominator: $\frac{1}{y} - \frac{1}{x}$

Now, let's find a common denominator for the fractions in the numerator:

1. The first fraction in the numerator is $\frac{x^2}{xy^2}$. To have a common denominator with the second fraction, we can express it with a denominator of $xy^2$. So, we multiply both the numerator and denominator of the first fraction by $y^2$, which gives us $\frac{x^2y^2}{xy^2}$.

2. The second fraction in the numerator is $-\frac{1}{x}$. To have a common denominator with the first fraction, we can express it with a denominator of $xy^2$. So, we multiply both the numerator and denominator of the second fraction by $y^2$, which gives us $-\frac{y^2}{xy^2}$.

Now, the expression becomes:

$\frac{\frac{x^2y^2}{xy^2} - \frac{y^2}{xy^2}}{\frac{1}{y} - \frac{1}{x}}$

Simplify further:

$\frac{x^2 - y^2}{\frac{1}{y} - \frac{1}{x}}$

Now, let's find a common denominator for the fractions in the denominator:

Denominator: $\frac{1}{y} - \frac{1}{x}$

To find a common denominator, multiply the second fraction by $\frac{y}{y}$:

$\frac{1}{y} - \frac{y}{xy}$

Now, the expression becomes:

$\frac{x^2 - y^2}{\frac{1}{y} - \frac{y}{xy}}$