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Jermey subtracted the following rational expressions. his teacher told him that his answer was incorrect. explain jeremys error in the simplification process and provide the correct results.

2x^2-10\x-5 - x^2+15\x-5 = x^2+5\x-5

User Jaromir
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1 Answer

7 votes

This is likely what Jeremy did


\frac{2\text{x}^2-10}{\text{x}-5}-\frac{\text{x}^2+15}{\text{x}-5}\\\\\frac{2\text{x}^2-10-\text{x}^2+15}{\text{x}-5}\\\\\frac{\text{x}^2+5}{\text{x}-5}\\\\

The error happens in line 2

This is what his steps should be


\frac{2\text{x}^2-10}{\text{x}-5}-\frac{\text{x}^2+15}{\text{x}-5}\\\\\frac{2\text{x}^2-10-(\text{x}^2+15)}{\text{x}-5}\\\\\frac{2\text{x}^2-10-\text{x}^2-15}{\text{x}-5}\\\\\frac{\text{x}^2-25}{\text{x}-5}\\\\\frac{(\text{x}-5)(\text{x}+5)}{\text{x}-5}\\\\\text{x}+5

On the 2nd step, we subtract all of (x^2+15) and not just the x^2 part. The negative distributes to each term in step 3. Then we combine like terms, factor and cancel out the (x-5) terms.

Therefore,
\frac{2\text{x}^2-10}{\text{x}-5}-\frac{\text{x}^2+15}{\text{x}-5}=\text{x}+5 is an identity as long as
\text{x} \\e 5 to avoid a division by zero error.

User Luis Herrera
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3.8k points