Can someone please provide an example problem showing multiplying and dividing rational expressions? I'm trying to get ready for
a DBA tomorrow. Thank you!
2 answers:
Step-by-step explanation:
To multiply rational expressions, simply multiply the numerators together (the tops) and the denominators together (the bottoms).
For example:
![\frac{x+a}{y+b}\times\frac{x+c}{y+d}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%2Ba%7D%7By%2Bb%7D%5Ctimes%5Cfrac%7Bx%2Bc%7D%7By%2Bd%7D)
![= \frac{(x+a)(x+c)}{(y+b)(y+d)}](https://tex.z-dn.net/?f=%3D%20%5Cfrac%7B%28x%2Ba%29%28x%2Bc%29%7D%7B%28y%2Bb%29%28y%2Bd%29%7D)
![=\frac{x^{2}+ax+cx+ac}{y^{2}+by+dy+bd}](https://tex.z-dn.net/?f=%3D%5Cfrac%7Bx%5E%7B2%7D%2Bax%2Bcx%2Bac%7D%7By%5E%7B2%7D%2Bby%2Bdy%2Bbd%7D)
To divide by a rational expression, multiply by its reciprocal. In other words, flip the fraction, then multiply.
For example:
![\frac{x+a}{y+b}\div\frac{x+c}{y+d}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%2Ba%7D%7By%2Bb%7D%5Cdiv%5Cfrac%7Bx%2Bc%7D%7By%2Bd%7D)
![=\frac{x+a}{y+b}\times\frac{y+d}{x+c}](https://tex.z-dn.net/?f=%3D%5Cfrac%7Bx%2Ba%7D%7By%2Bb%7D%5Ctimes%5Cfrac%7By%2Bd%7D%7Bx%2Bc%7D)
![=\frac{(x+a)(y+d)}{(x+c)(y+b)}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B%28x%2Ba%29%28y%2Bd%29%7D%7B%28x%2Bc%29%28y%2Bb%29%7D)
![=\frac{xy+dx+ay+ad}{xy+bx+cy+bc}](https://tex.z-dn.net/?f=%3D%5Cfrac%7Bxy%2Bdx%2Bay%2Bad%7D%7Bxy%2Bbx%2Bcy%2Bbc%7D)
I hope this helps... good luck
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