Week 15- Precalc 11

The most important point I learned in this week was solving rational equations.

Situation 1: Each side of equal sign only one fraction. (In this situation, we can simply use cross multiply.)

Ex: $\frac{x-2}{5}\cdot\frac{x-1}{3}$

$3x-6=5x-5$ , $-1=2x$ , $x=\frac{-1}{2}$

Situation 2: One side of equal sign have more than one fractions.

Step 1: Eliminate all fractions. (each fractions multiply the smallest common denominator)

Step 2: Solve the simplified equation.

Step 3: Get the result.(include the non-permissible value of x)

Ex: $\frac{5}{x+3}\cdot\frac{2}{x^2+9}=\frac{4}{x-3}$

$5\cdot(x-3)\cdot2=4\cdot(x+3)$ , $5x-4x=12+13$ , $x=25$

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