This week in Precalculus 11, we learned about solving rational equations.

Rational equation: an equation containing rational expressions.

To solve a rational equation, we first identify non-permissible values. One way to solve a rational equation is to multiply each term by the lowest common denominator, then solve normally. Another is if 2 fractions are equal to eachother and have either the same numerators or same denominators, their numerators/denominators must also match. We then check for extraneous roots, or non-permissible values.

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This week in Precalculus 11, we started the Rational Expressions and Equations Unit. We first learned about equivalent rational expressions.

rational expression: a fraction with polynomials in the numerator & denominator

non-permissable value: variable values making the denominator 0

To determine the non-permissable values, we equate the denominator to 0 and solve the equation.

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To simplify a rational expression, we first factor the numerator and denominator. We then identify the non-permissable values. Last, we cancel out identical pairs of numerators and denominators.

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This week in Precalculus 11, we learned about graphing reciprocals of linear functions.

reciprocal: numerator and denominator are switched

linear function: an equation in 2 variables with degree 1

asymptote: barrier lines of a graph

To graph the reciprocal of a linear function, we first graph its parent function. We then find the points on the graph where y = 1 and y = -1, and the vertical and horizontal asymptotes. In most cases, the horizontal asymptote is y = 0. The vertical asymptote is the x-intercept. We then use these points to draw a 2-part graph known as a hyperbola. The asymptotes act as barriers.

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