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Example Questions
Example Question #1 :How To Find The Solution Of A Rational Equation With A Binomial Denominator
For the equation, what is(are) the solution(s) for?
可以考虑(x 7)(3) = 0。因此,x-7 = 0 and x-3 = 0. Solving for x in both cases, gives 7 and 3.
Example Question #2 :Binomial Denominators
Simplify:
In order to begin this kind of a problem, it's key to look at parts of the rational expression that can be simplified.
In this case, the denominator is an already-simplified binomial; however, the numerator can be factored through "factoring by grouping." This can be a helpful idea to keep in mind when you come across a polynomial with four terms and simplifying is involved.
can be simplified first by removing the common factor offrom the first two terms and the common factor offrom the last two terms:
This leaves two terms that are identicaland their coefficients, which can be combined into another term to complete the factoring:
Consider the denominator; the quantityappears, so thein the numerator and in the denominator can be cancelled out. The simplified expression is then left as.
Example Question #2 :How To Find The Solution Of A Rational Equation With A Binomial Denominator
Simplify:
In order to begin this kind of a problem, it's key to look at parts of the rational expression that can be simplified.
In this case, the denominator is an already-simplified binomial; however, the numerator can be factored.
The roots will be numbers that sum up tobut have the product of.
The options include:
When these options are summed up:
We can negate the last three options because the first option ofandfulfill the requirements. Therefore, the numerator can be factored into the following:
Because the quantityappears in the denominator, this can be "canceled out." This leaves the final answer to be the quantity.