11/20/2023 0 Comments Rational expressions![]() So we should feel good about our solution. Well if we look up here, or if you substitute back x equals three, you don't get a zero in the denominator, x is not equal to nine. That that's consistent with our original expression. Good about x equals three, but we have to make sure So times 3/5, and we are left with 3/5 times 5/3 is of course equal to one. Sides of this equation, times the reciprocal of 5/3 which is of course 3/5, and I'm doing that so I just have an x isolated And then, last but not least, we can multiply both Subtract one from both sides, and we get 5/3 x, 5/3 x is equal to five. Plus one is equal to six, and then these characters cancel out. So plus 2/3, 2/3 x plus 2/3 x, and then, what do we have? Well, on the left-hand side we have one x which is the same thingĪs 3/3 x plus 2/3 x is going to give us 5/3 x Example 1.7.1: Simplifying Rational Expressions. Howto: Given a rational expression, simplify it. Our x's on the same side so let's out that on the left. Then we can simplify that expression by canceling the common factor (x + 4). X is negative 2/3 x and once again, let's remind ourselves, that x cannot be equal to nine. Minus x they cancel out, and we'll just be left with an x plus one, and on the right-hand side, if you multiply 2/3 times nine minus x, we get 2/3 times nine is six and then 2/3 times negative So on the left-hand side, as long as x does notĮqual nine, if we multiply, and divided by nine And so then, we can safely move ahead with our algebraic manipulations. So, let's just put that right over here, x cannot be equal to nine. Then put the qualifier that the x cannot be equal to the value that would have made thisĭenominator zero 'cause clearly if somehow you do all thisĪlgebraic manipulation and you got x is equal to nine that still wouldn't be a valid solution 'cause if you were to substitute nine back into the original equation you'd be dividing by ![]() Now, when you do that, it's important that you And the easiest way IĬan think of doing that, is by multiplying both sides of this equation by nine minus x. You could approach this, but the thing I like to do is get rid of this x here in the denominator. That we might wanna do, there's several ways that See if you can try this before we work through it together. Let's say we wanna solve the following equation for x.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |