Write each rational expression in lowest terms.$$rac{20 r+10}{30 r+15}$$...

Write each rational expression in lowest terms.
$$\frac{25 p^{3}}{10 p^{2}}$$

Okay today, I want to talk about simplifying rational expressions. So let's say we've got this rational expression. Rational expressionist means to ratio of two expressions, the fraction if you would ratio to expression. So in this rational expression, we're gonna have a 25 p cubed 25 t to the third power in the numerator and in the denominator, let's have 10 p square 10. He is where? All right, so to simplify irrational expression to write it in its lowest terms. What we want to do is we wanna do prime factory ization of the numerator prime factor ization of the denominator and eliminate common factors. So 25 is that see, it's five times five. Those are both prime numbers. So 25 it's five times, but so we could rewrite 25 as its prime factors by time spot. Now Peter, the third power is the variable p to the third power that exploded. Three means that the base is a factor three times. So this is records. There's a multiplication between the number of the bird. Topi to the third power based P is a factor. One, two, three cups a pee to the third Power is something teen times peeing time. Speak now in my denominator Got 10? Well, let's see half tennis by so tell us to times fought. Those are both prime numbers were prime numbers just any number that's only divisible by one and itself So and then pee to the second power means exponents to pee. The base P is a factor two times. So peace word is just pee. I'm speak. So to simplify this, remember that the factors if they're in the Newman of the nominated Bacon bacon basically eliminate one another because think about what is five divided by five. Well, five goes into 51 time, so it's like factoring out of what sent here. P goes into P one time. He's not equal to zero, and it can't be equal to zero. Or you would have undefined to grind by zero error with the peace word here. So he is not equal to zero. We know that so we can divide p by itself and it's also what whatever p is other than zero clue as a result one time. So what? See, what are we left with? Well, the these fires back to that. But we still have a five in the numerator, and we still have this p of the new writer. So we still have five p in the numerator and in the denominator. Well, everything went away except for the two. So I can simplify 25 p to the third power over 10 p to the second tower. That rational expression as five p over, too, where we could even pull the p that very well p out in front. You know, after the Fraction five have so another way we could write. This is 2.5 p or five over two. Okay? And I hope that helps

Problem. One sister, right? A fraction Simplest terms said R squared minus R minus six About about our square plus plus R minus 12 Teoh to simplify destruction. I'm gonna first factor microelectronics. So my car drunk and the name writers gonna become our minus three times our money our plus two and our denominators gonna become ar minus three times are close for AR minus three is will cancel leaving us with our plus to do about about our close for okay.

Hey, guys. So we need to write this rational expression in Blois terms, so 18 can be written as to times three times three right and are cute. Can be factor into our times. Far terms far. Well, for six. It can be factoring two twos. Time three and arches are okay, so we can totally cancel this out. And this hour. And finally, which was have three r squared. Pass it. Thank you so much for listening.

Hey guys, let's try to simplify this. So, for the numerator, what is a common factor? How about five? So we'll bring five out Will just have five hour plus four. Right? And in the denominator, it will bring three out, which is have our A plus for two. So now our plus four is in the top and in the bottom us. Well, so it begins holdout. We'll just have 5/3 as I will find the answer. Thank you so much for listening.