Algebra: Chapter 10, Lesson 1, page 432.
Simplifying Rational Expressions
A rational expression is a quotient of 2 polynomials. A rational expression always indicates division. A rational expression is in simplest form when the numerator and denominator have NO COMMON factors other that `1` or `−1`.
Factor the numerator and the denominator and see what terms can be cancelled. For example:
`(5x-10)/(5x)=(5(x−2))/(5x)`. We can cancel the `5/5` in the numerator and denominator, leaving us with `=(x-2)/x`
and
`(y^2+3y+2)/(y^2-1)`
The numerator using the box, factors to `(y+1)((y+2)` and the denominator being the difference of 2 squares at `(y+1)(y-1)`, we have:
`=((y+1)(y+2))/((y+1)(y-1))`. In this example, then we can cancel the `(y+1)/(y+1)` (in the numerator and denominator), leaving us with just `=(y+2)/(y-1)`
AND, here is a link from purplemath with more examples.
Two of tonight’s homework problems solved by MrE are here! Just click it!
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Algebra 1a: Chapter 7 Review for Algebra Benchmark (#9)
Algebra Skills Practice 19/20 and the Benchmark #2 Practice and Review were started in class. The end of the Chapter Review is a good overview and practice of the entire chapter.
Remember, to solve problems using the slope-intercept formula, `y = mx + b`, you need to have (or solve first for) the slope, then using one of the ordered pairs given `(x, y)` solve for the y-intercept, b.
Given the slope `m`, and the y-intercept `b`, we can develop the equation by plugging in the values for the slope and the y-intercept.
An equation perpendicular to the given one will have to have its slope be the negative reciprocal for the product to be -1. In other words, `m_1 * m_2 = -1`
A new equation that has to be parallel to the given one, must have its slope be exactly the same, `m_1 = m_2`!