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homework | section 1.6 rational expressions
webwork / mat 1023 fall 2025 / sec 1.6 rational expressions / 1
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sec 1.6 rational expressions: pro
(1 point)
add or subtract the rational expressions to a single rational expression and
\\(\frac{1}{y - 1}-\frac{2}{y^{2}-1}=\square\\)
note: separate your answers by comma, and use != to type the \\(\
eq\\) symbol.
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Explanation:

Step1: Factor the denominator

Factor $y^{2}-1$ using the difference - of - squares formula $a^{2}-b^{2}=(a + b)(a - b)$. So, $y^{2}-1=(y + 1)(y - 1)$.
The given expression becomes $\frac{1}{y - 1}-\frac{2}{(y + 1)(y - 1)}$.

Step2: Find a common denominator

The common denominator of the two fractions is $(y + 1)(y - 1)$. Rewrite $\frac{1}{y - 1}$ with the common denominator: $\frac{1}{y - 1}\times\frac{y + 1}{y + 1}=\frac{y+1}{(y + 1)(y - 1)}$.
The expression is now $\frac{y + 1}{(y + 1)(y - 1)}-\frac{2}{(y + 1)(y - 1)}$.

Step3: Subtract the numerators

When the denominators are the same, we subtract the numerators: $\frac{y + 1-2}{(y + 1)(y - 1)}=\frac{y-1}{(y + 1)(y - 1)}$.

Step4: Simplify the fraction

Cancel out the common factor $(y - 1)$ in the numerator and denominator (assuming $y
eq1$). We get $\frac{1}{y + 1},y
eq1,y
eq - 1$.

Answer:

$\frac{1}{y + 1},y
eq1,y
eq - 1$