Mathematics, 17.04.2021 14:00 girlhooper4life11

Simplify the expression: (in the image attached)

Answers: 1

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Answer from: Tren17

Step-by-step explanation:

Hey there!

$\tt{\dfrac{\dfrac{1}{x^2} + \dfrac{2}{y}}{\dfrac{5}{x} - \dfrac{6}{y^2}}}$

So, what we can do here is first take the Least Common Multiple here, on both Numerator and Denominator.

$\tt{\dfrac{\dfrac{y + 2y^2 (1)}{x^2 y (2)}}{\dfrac{5y^2 - 6x (3) }{xy^2 (4)}}}$

[The number in brackets is for the next step :-

When we will further simplify it, we will multiply 1st with 4th and 2nd with 3rd.

$\tt{\dfrac{y + 2y^2 \times xy^2 }{x^2 y \times 5y^2 - 6x }}$

$\tt{\dfrac{y + 2y^2 \times y }{x \times 5y^2 - 6x }}$ is the framed answer.

Answer from: angel34emb

$\frac{y(y+2x^2)}{x(5y^2-6x}$

Step-by-step explanation:

Lets do the numerator and denominator seperately:

Numerator:

1/x^2 + 2/y

Find common denominator and add these 2 fractions:

This is x^2y (I just multiplied the 2 denominators together’

Now, do what you have done to x^2 to make it x^2y, ie. multiplied by y, to the 1. This = y

And do what you have done to y to make it x^2y, ie. multiplied by x^2, to the 2. This = $2^{2}$

Now, arrange all numbers we have found into the correct order in the fraction. This is:

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

Denominator:

5/x - 6/y^2

Find the common denominator and subtract these two fractions:

This is xy^2

Now, do what you have done to x to make it xy^2, ie. multiply by y^2, to the 5. This = 5y^2

And do what you have done to the y^2 to make it xy^2, ie. multiply by x, to the 6, this is = 6x

Now, arrange all the numbers we have found into the correct order in the fraction

$\frac{5y^{2}-6x}{xy^2}$

Now that we have the numerator and the denominator, we can solve the equation.

The original question asks us to divide the 2 fractions, so:

$\frac{y+2x^{2}}{x^{2} y}$ divided by $\frac{5y^{2}-6x}{xy^2}$

For the division of fractions, you just have to multiply the inverse of the 2nd fraction by the first, so

$\frac{y+2x^{2}}{x^{2} y}$ x $\frac{xy^2}{5y^2-6x}$

Use cross multiplication to simplify the above expression to:

$\frac{y(y+2x^2)}{x(5y^2-6x}$

Hope this helps, sorry its long ...

Answer from: Quest

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)

Answer from: Quest

answer: i believe the answer is e

step-by-step explanation:

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Simplify the expression: (in the image attached)
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