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Simplifying expressions
Cancelling common factors and combining fractions.
To simplify a rational expression, factor the numerator and the denominator and cancel what they share: remembering the cancelled factor still forbids the value that made it zero. Sums of fractions are combined over a common denominator, just like numbers.
Voorbeeld van werk · simplify (x^2-1)/(x-1)
Stap voor stap
- \frac{x^{2} - 1}{x - 1}
Start from the expression.
- x + 1
Factor numerator and denominator and cancel common factors.
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Hoe: Simplifying expressions
- Start from the expression.
- Factor numerator and denominator and cancel common factors.
Vragen die mensen stellen
What does it mean to solve an equation?
To find every value of the unknown that makes both sides equal. Each step is an operation applied to both sides that keeps the solution set the same, until the unknown stands alone.
Why do I sometimes get two answers?
A quadratic can cross the axis twice, so it can have two solutions. A degree-n polynomial has up to n. The graph shows where each one comes from.
How do I know whether to factor or use the quadratic formula?
Try factoring for a few seconds: look for two numbers that multiply to a·c and add to b. If nothing obvious appears, the discriminant b² − 4ac tells you how many real roots there are, and the formula finds them without guessing.
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