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BartSMP [9]
3 years ago
14

(Please Hurry!) Which expression is equivalent to the following complex fraction?

Mathematics
1 answer:
galben [10]3 years ago
6 0

Answer:

The expression equivalent to the given complex fraction is

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

Step-by-step explanation:

An easy way to solve the complex fraction is to solve the numerator and denominator separately.

Numerator:

\frac{-2}{x} + \frac{5}{y}\\ = \frac{-2y + 5x}{xy}

Denominator:

\frac{3}{y} + \frac{-2}{x}\\ = \frac{3x - 2y}{xy}

Solving the complex fraction:

[\frac{-2}{x} + \frac{5}{y}] / [\frac{3}{y} + \frac{-2}{x}]\\= [\frac{-2y + 5x}{xy}] / [\frac{3x - 2y}{xy}]

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

Common terms in the numerator and denominator cancels each other(Cross multiplication) :

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

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We can see that both triangles are right angle triangle as per information given into picture. So we will prove that they are similar then use properties of similar triangle to find the value of d.

In triangle STV and triangle XWV:

∠STV = ∠XWV { both are equal to 90 degree}

∠TVS = ∠WVX { vertically opposite angles are equal}

Hence by AA (Angle Angle) similarity postulate of the triangles, It is proved that triangle STV and triangle XWV are similar.

We know that ratio of corresponding sides of similar triangles are equal so we can write:

\frac{ST}{XW}=\frac{TV}{WV}

\frac{350}{d}=\frac{400}{180}

350*180=400d

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divide both side by 400

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Find the integral, using techniques from this or the previous chapter.<br> ∫x/25-9x^2 dx.
kipiarov [429]

Answer:

\frac{x^{2} }{50} - 3x^{3} +C

Step-by-step explanation:

we are to find the integral of  \frac{x}{25} -9x^{2} dx.

we will integrate by using the principle of integration of a sum or difference of two functions by integrating them separately.

∫x/25-9x^2 dx = \frac{x^{2} }{2*25}- 9\frac{x^{3} }{3} +C

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