Simplifying Algebraic Fractions: Non-Monic Expressions

Transcript

Now I’m going to factorize them individually again but they’re not monic quadratic, so be very careful! So starting with here, I’m going to use x and 2x and the other one will be 1 which becomes 2x and negative 1, negative x and 2x minus x is x which is right.

Now for the denominator, I’m going to use x and 2x again, and here, I’m going to use negative 2 which becomes negative 4x, and negative 1 which is negative x. Add them, we get negative 5x which is correct. Same over here. This time I’m going to use x and 3x because that’s 3x squared, isn’t it? So I’m going to use negative 2, it’s negative 6x and negative 1, negative x.

Add them together. We get negative 7x which is right. Now one more, I’ve got x and 3x again because that’s 3x squared and I’m going to use positive 1, 3x and negative 1 for the other one. So negative x. Add them! We get 2x. Correct!! Now replace them all in, just like that. I just put them all in. Put that in there, that there, that there and that there, okay? So I don’t have to go through everything. And let’s cancel! Common, what else, common, common, and common. Everything is gone! So what’s the answer?

Simply one. Don’t say zero. I know a lot of people say zero because everything’s gone but it’s all one because they’re all the same we cancel everything out only one is left. One is the solution. Please don’t say zero, okay? That was a long working out for such a simple answer but that’s how it works out after we do all of those factorizations, okay? So that was the end of this part.

 

Algebra Algebraic Fractions Arc Binomial Expansion Capacity Common Difference Common Ratio Differentiation Divisibility Proof Double-Angle Formula Equation Exponent Exponential Function Factorials Factorise Functions Geometric Sequence Geometric Series Index Laws Inequality Integration Kinematics Length Conversion Logarithm Logarithmic Functions Mass Conversion Mathematical Induction Measurement Perfect Square Perimeter Prime Factorisation Probability Proof Pythagoras Theorem Quadratic Quadratic Factorise Rational Functions Sequence Sketching Graphs Surds Time Transformation Trigonometric Functions Trigonometric Properties Volume




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