Answers
Step-by-step explanation:
Hey there!
[tex]\tt{\dfrac{\dfrac{1}{x^2} + \dfrac{2}{y}}{\dfrac{5}{x} - \dfrac{6}{y^2}}}[/tex]
So, what we can do here is first take the Least Common Multiple here, on both Numerator and Denominator.
[tex]\tt{\dfrac{\dfrac{y + 2y^2 (1)}{x^2 y (2)}}{\dfrac{5y^2 - 6x (3) }{xy^2 (4)}}}[/tex]
[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.
[tex]\tt{\dfrac{y + 2y^2 \times xy^2 }{x^2 y \times 5y^2 - 6x }}[/tex]
[tex]\tt{\dfrac{y + 2y^2 \times y }{x \times 5y^2 - 6x }}[/tex] is the framed answer.
Answer:
[tex]\frac{y(y+2x^2)}{x(5y^2-6x}[/tex]
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 = [tex]2^{2}[/tex]
Now, arrange all numbers we have found into the correct order in the fraction. This is:
[tex]\frac{y+2x^{2}}{x^{2} y}[/tex]
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
[tex]\frac{5y^{2}-6x}{xy^2}[/tex]
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:
[tex]\frac{y+2x^{2}}{x^{2} y}[/tex] divided by [tex]\frac{5y^{2}-6x}{xy^2}[/tex]
For the division of fractions, you just have to multiply the inverse of the 2nd fraction by the first, so
[tex]\frac{y+2x^{2}}{x^{2} y}[/tex] x [tex]\frac{xy^2}{5y^2-6x}[/tex]
Use cross multiplication to simplify the above expression to:
[tex]\frac{y(y+2x^2)}{x(5y^2-6x}[/tex]
Hope this helps, sorry its long ...
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