Rational Equations Using Proportions
You are now ready to solve rational equations! There are two main methods you will learn to solve rational equations:
- Lowest common denominators
This Concept will focus on cross-products. When two rational expressions are equal, a proportion is created and can be solved using its cross-products.
Let's solve the following rational equations:
Notice that this equation has a degree of two; that is, it is a quadratic equation. We can solve it using the quadratic formula.
Start by cross multiplying:
Since this equation has a squared term as its highest power, it is a quadratic equation. We can solve this by using the quadratic formula, or by factoring.
Since there are no common factors, start by finding the product of the coefficient in front of the squared term and the constant:
What factors of -6 add up to 5?
That would be -6 and 1, since -6+1=-5
Use the Zero Product Principle:
First, let's set up an equation using the given information. The distance traveled in a specific amount of time can be written as a fraction of the distance over the time.
Now, we can cross multiply.
Solve the following equations.
- Divide: −2910÷−158.
- Solve for g:−1.5(−345+g)=20120.
- Find the discriminant of 6x2+3x+4=0 and determine the nature of the roots.
- Simplify 6b2b+2+3.
- Simplify 82x−4−5xx−5.
- Divide: (7x2+16x−10)÷(x+3).
- Simplify (n−1)∗(3n+2)(n−4).
To see the Review answers, open this PDF file and look for section 12.8.