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adding of these fractions..

Schüler

Tags: Mathematik

RASTA aktiv_icon

19:22 Uhr, 29.09.2022

Hi, I need help to add these two fractions together and simplify them till they can not be simplified any more

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

I have found the common denominator to be 2xy
but I am having difficulties in finding the numerators, like,

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

/(2xy)

+

/(2xy)

I will need a hint to go forward,
thanks

Für alle, die mir helfen möchten (automatisch von OnlineMathe generiert):
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pivot aktiv_icon

19:31 Uhr, 29.09.2022

Hello,

for the first fraction you want

\frac{y}{x} = \frac{?}{2 x y}

To get a denominator

2 x y

you have to expand the fraction by

2 y

\frac{y}{x} \cdot \frac{2 y}{2 y} = \frac{2 y y}{2 x y} = \frac{2 y^{2}}{2 x y}

Can you expand

\frac{3}{2 y}

so that the denominator is

2 x y

?

greetings,
pivot

N8eule

23:04 Uhr, 29.09.2022

Aus dem Zusammenhang wage ich erheblichen Zweifel, ob deine Aufgabe eigentlich heißen wollte:

a)

\frac{y}{x} + \frac{3}{2} \cdot y

oder doch eher

b)

\frac{y}{x} + \frac{3}{2 \cdot y}

Kannst du das nochmals klar stellen?

supporter aktiv_icon

11:30 Uhr, 30.09.2022

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

= \frac{y \cdot 2 + 3 y \cdot x}{2 x} = \frac{y \cdot (2 + 3 x)}{2 x}

RASTA aktiv_icon

23:48 Uhr, 06.10.2022

Thanks everyone for the support.

Mathe45

23:56 Uhr, 06.10.2022

We rather assume that this is the correct specification and therefore of course also brings a different result:

RASTA aktiv_icon

00:11 Uhr, 07.10.2022

It is like in the thread. exactly like that.

another way possible is by cross-multiplying

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

2y^2/2xy

+ 3 x

/2xy

= (2 y^{2} +

3x)/(2xy)

RASTA aktiv_icon

00:16 Uhr, 07.10.2022

8neule is right

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

Mathe45

00:20 Uhr, 07.10.2022

And your result ?
Write it down so we can READ it.

" eddy2013 " ???

RASTA aktiv_icon

00:30 Uhr, 07.10.2022

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

2y^2/(2xy)

+

3x/(2xy)

= 2 y^{2} +

3x/(2xy)

RASTA aktiv_icon

00:38 Uhr, 07.10.2022

applying the fraction rule was easier
the LCM was

c

the a and

b

came form the elements that were cross-multiplied

the fraction rule

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

RASTA aktiv_icon

00:48 Uhr, 07.10.2022

supporter, this question is for you. If that were the case, (which it is not),
I am not getting the part after the equal sign, the right side.
I don't understand the operation you performed there.
how do you simplify the left side expression to

y \cdot (2 + 3 x)

the

2 x, I

understand, but not the numerator, how you got that out of

y \cdot 2 + 3 y \cdot x

supporter aktiv_icon

05:05 Uhr, 07.10.2022

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

The common denominator is

2 x,

which must be generated for both fractions.
Expand them in order to get to that denominator.
The first one must be expanded by

2,

the second one by

x

.
Some call that "cross multiplication", in German: über Kreuz multiplizieren.
This often is the easiest way of forming the main denóminator.

RASTA aktiv_icon

23:36 Uhr, 07.10.2022

thanks to all!!

RASTA aktiv_icon

23:38 Uhr, 07.10.2022

Got it now.

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