To add algebraic expressions to fractions, you typically need to find a common denominator and then combine the numerators. The referenced YouTube video, "Adding Algebraic Fractions," illustrates this process. Specifically, if you have a fraction like a/x, and you want to add it to another fraction, you might need to multiply the numerator and denominator of a/x by a certain expression (like y, as mentioned in the reference) to achieve a common denominator.
Here's a breakdown of the process:
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Find the Least Common Denominator (LCD): Determine the LCD for all the fractions you intend to add. This might involve factoring the denominators.
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Rewrite Each Fraction: Adjust each fraction, multiplying both the numerator and denominator by the appropriate factor, so that each fraction has the LCD as its new denominator. As seen in the reference, you might times both the top and the bottom of the numerator and denominator of
a/xbyy. This is a vital step to obtain a common denominator. -
Add the Numerators: Once all the fractions have the same denominator, you can add their numerators. Keep the common denominator.
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Simplify: Simplify the resulting fraction, if possible, by factoring and canceling common factors.
Example:
Let's say you want to add the algebraic fractions: (a/x) + (b/y)
- The least common denominator (LCD) is
xy. - Rewrite each fraction with the LCD:
(a/x)becomes(a*y)/(x*y)(b/y)becomes(b*x)/(y*x)
- Add the numerators:
(ay + bx) / (xy)
