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$${2x^2+5x-3\over16x^2+26x+9}\cdot{10x^2+13x+4\over5x^2+11x-12}\cdot{35x^2-38x+8\over x^2+x-2}$$ Please help me. I'm having a hard time with 3 terms.

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2 Answers

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HINT: Factor!

$${2x^2+5x-3\over16x^2+26x+9}\cdot{10x^2+13x+4\over5x^2+11x-12}\cdot{35x^2-38x+8\over x^2+x-2} $$ $$= \dfrac{(2x -1)\color{red}{\bf (x+3)}}{(8x+9)\color{blue}{\bf (2x + 1)}}\cdot \dfrac{(5x + 4)\color{blue}{\bf (2x + 1)}}{\color{green}{\bf (5x-4)}\color{red}{\bf (x+3)}} \cdot \dfrac{(7x - 2)\color{green}{\bf (5x - 4)}}{(x+2)(x-1)}$$

Cancel common factors in numerator and denominator.

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Factor, and then cancel, BEFORE multiplying.

I see students faced with $\dfrac{20\cdot19\cdot18\cdot17\cdot16\cdot15}{6\cdot5\cdot4\cdot3\cdot2\cdot1}$ grabbing their calculators and evaluating the large number in the numerator. But the $20$ cancels $5\cdot4$ and the $18$ cancels $6\cdot3$ and $\dfrac{16}{2}=8$, so you've got $19\cdot17\cdot2\cdot15$.

The same thing applies to polynomials. I've seen students faced with expressions like the one in this problem multiplying out the polynomials in the numerator, and similarly in the denominator. You're guaranteed to get lost that way.

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