Mathematics, 03.08.2019 20:50 jasmineharris121

Which expression is equivalent to the following complex fraction? -2/x+5/y/3/y-2/x

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The way how the question entered here, I have to make few assumptions to answer. Hoping that one of the below assumption is your actual problem.

Assumption 1: If your complex fraction is given as below

$\frac{\frac{-2}{x+\frac{5}{y}}}{\frac{3}{y-\frac{2}{x}}}$

Then we need to write $x+\frac{5}{y}$ as a single fraction by rewriting x as a fraction $\frac{x}{1}$ , then multiplying y on both top and bottom of that fraction to get $\frac{xy}{y}$ .

We can rewrite $x+\frac{5}{y}$ as $\frac{xy}{y} +\frac{5}{y}$ which will be equal to $\frac{xy+5}{y}$ .

In the same way $y-\frac{2}{x} =\frac{xy}{x}-\frac{2}{x}=\frac{xy-2}{x}$

When dividing fractions we need to flip the bottom and multiply with top:

So $\frac{-2}{\frac{xy+5}{y}}$ $\frac{-2}{1} * \frac{y}{xy+5}=\frac{-2y}{xy+5}$

In the same way, $\frac{3}{\frac{xy-2}{x}} =\frac{3}{1} *\frac{x}{xy-2} =\frac{3x}{xy-2}$

Applying the same logic of flipping the fraction and multiplying with the top, we get the below final expression.

$\frac{\frac{-2y}{xy+5} }{\frac{3x}{xy-2} } =\frac{-2y}{xy+5}*\frac{xy-2}{3x}=\frac{-2y(xy-2)}{3x(xy+5)}=\frac{4y-2xy^{2}}{15x+3x^{2}y}$

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Assumption 2: If your complex fraction is given as below

$\frac{\frac{-2}{x} +\frac{5}{y} }{\frac{3}{y} -\frac{2}{x} }$

The LCD of both the top part and bottom part is 'xy', we can multiply that in both top and bottom part to simplify the given complex fraction as below:

$\frac{xy(\frac{-2}{x}+\frac{5}{y}) }{xy(\frac{3}{y}-\frac{2}{x}) } =\frac{\frac{-2xy}{x}+\frac{5xy}{y}}{\frac{3xy}{y}-\frac{2xy}{x}}$

Cancelling the common factors in both top and bottom of each fraction we will get the below simplified fraction

$\frac{-2y+5x}{3x-2y} =\frac{5x-2y}{3x-2y}$

Answer from: kaitlyn114433

The expression expressed as a single fraction is expressed as $=\frac{-2y(yx-2)}{3x(yx+5)}$

Given the expression:

$\dfrac{\frac{-2}{x+\frac{5}{y} } }{\frac{3}{y-\frac{2}{x} } }$

First, we need to write the denominators as a single fraction as shown:

$x+\frac{5}{y} = \frac{yx+5}{y}$

Similarly for $y-\frac{2}{x}=\frac{yx-2}{x}$

Substitute the resulting function into the given function, we will have:

$=\dfrac{\frac{-2}{\frac{yx+5}{y} } }{\frac{3}{\frac{yx-2}{x} } }\\\\=\dfrac{\frac{-2y}{yx+5} }{\frac{3x}{yx-2} } \\=\frac{-2y}{yx+5}\times\frac{yx-2}{3x} \\=\frac{-2y(yx-2)}{3x(yx+5)}$

This shows that the expression expressed as a single fraction is expressed as $=\frac{-2y(yx-2)}{3x(yx+5)}$

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Answer from: Quest

a net is a diagram that shows a “flattened” view of a solid. in a net, each face and base is shown with all of its dimensions. a net can also serve as a pattern to build a three-dimensional solid.

a pyramid is a three-dimensional object with a base that is a polygon and triangular faces that meet at one vertex.

" the net of a triangular pyramid consists of four triangles. the base here we are given of the pyramid is a equilateral triangle, and the lateral faces are also triangles "

Answer from: Quest

could you provide figure.

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Which expression is equivalent to the following complex fraction? -2/x+5/y/3/y-2/x...

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