Q&A for How to Simplify Algebraic Fractions

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Why does it work exactly like this all the time?

Donagan

Top Answerer

Because the properties of and operations with numbers never change.

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When factoring algebraic fractions, how do I know which one will have a plus or minus sign? For example, 12x^2 + 43x+ 35 / 6x^2 +5x - 21?

Donagan

Top Answerer

This is known as "solving by inspection." In other words, you just look at ("inspect") the expression you're factoring, and choose plus and minus signs so that the factors, when multiplied together, result in the original expression. In the example cited, 12x² + 43x +35 factors into (3x + 7) and (4x + 5). 6x² + 5x - 21 factors into (3x + 7) and (2x - 3). In each case the signs were chosen so that multiplying the factors together would result in the original expression. In this case there is a factor of (3x + 7) in both the numerator and denominator, so that they cancel each other. The final, simplified expression is (4x + 5) / (2x - 3).

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What if there's a question like this: (1–y²) / (–y² – y + 2)?

Donagan

Top Answerer

First simplify a little by factoring (-1) from both numerator and denominator: -(y²-1) / -(y²+y-2). The (-1)'s will cancel each other, and you're left with (y²-1) / (y²+y-2). Factor numerator and denominator: [(y+1)(y-1)] / [(y+2)(y-1)]. The two (y-1)'s cancel each other, and the final fraction is (y+1) / (y+2).

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How to simplify 17y/9?

Community Answer

That term is already in its simplest form.

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Question

Factorize (a - b)(a - b).

Community Answer

That expression is already factorized (or factored). In other words, it cannot be factorized (factored) any further. It can also be written as (a - b)².

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