Algebraic Fractions

7x/x^4y^7 + 3/x^6y^2

Do i need to find the common denominator?

Eyeball Problem

x^6 * y^7

"Prime Factors" are important. Pick a big enough exponent so that ALL denominators' needs are met.

so x^6 y^7 is our common denominator since we need prime factors?

Prime Factors is really a concept for Whole numbers, but that is the idea. Another way to say it is the pick the greatest exponent on each unique factor.

okay got that part, so what can i do with the 7x and 3?

Psychguy98 said:

okay got that part, so what can i do with the 7x and 3?

Click to expand...

ONCE MORE, your ORIGINAL post: 7x/x^4y^7 + 3/x^6y^2 needs brackets: 7x / (x^4y^7) + 3 / (x^6y^2 ).
If you're to "get the hang" of these, it is IMPORTANT that you UNDERSTAND bracketing :idea:

There is no "7x" involved: the 7x / (x^4y^7) becomes 7 / (x^3y^7) ;
so expression is now : 7 / (x^3y^7) + 3 / (x^6y^2) : do you "follow" that?

so then 7x^3 and 3y^5?

Back to your original question. Yes, finding a common denominator ot how you add fractions. Never question this gain.

You have two denominators:

x^4 * y^7 and x^6 * y^2

The common denominator is x^6 * y^7

Looking at each denominator separately:

x^4 * y^7 will need x^2

x^6 * y^2 will need y^5

Therefore:

\(\displaystyle \frac{7x}{x^{4}y^{7}}+\frac{3}{x^{6}y^{2}}\;=\;\frac{7x}{x^{4}y^{7}}\cdot \frac{x^{2}}{x^{2}}+\frac{3}{x^{6}y^{2}}\cdot \frac{y^{5}}{y^{5}}\)

This suggests that you MAY be on the right trakc, but since you are not speaking in complete sentences, it si very difficult to follow what you are doing.

Give a go at writing out the complete final answer. Use good notation. Add parentheses to emphasize intent and to be correct..

so x^2 and y^5 are our common denominators? How is that? because 6-4 = 2 and 7-2 = 5

Psychguy98 said:

so x^2 and y^5 are our common denominators? How is that? because 6-4 = 2 and 7-2 = 5

Click to expand...

RULE: x^a times x^b = x^(a+b) ; x^a divided by x^b = x^(a-b) ; tattoo that on your wrist :wink:

Psychguy98 said:

so x^2 and y^5 are our common denominators? How is that? because 6-4 = 2 and 7-2 = 5

Click to expand...

Among other things, you must listen to yourself. Think about this, "Common Denominators". Tell me what that possibly could mean. When adding fractions, you get ONE common denominator. That's why it's called "common".

In the example above (x^6)(y^7) is THE common denominator.