solve the rational equation, State the excluded values in the picture below

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25-10-2022
Mathematics

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solve the rational equation, State the excluded values in the picture below

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VivicaR746737 VivicaR746737 · Answer 1 · 2022-10-25T23:58:14+02:00

[tex]\begin{gathered} \frac{x+7}{x+4}-1=\frac{x+10}{2(x+4)} \\ \frac{x+7-(x+4)}{x+4}=\frac{x+10}{2(x+4)} \\ \frac{x+7-x-4}{x+4}=\frac{x+10}{2(x+4)} \\ \frac{3}{x+4}=\frac{x+10}{2(x+4)} \\ \text{cross multiply} \\ 3\times2\times(x+4)=(x+4)(x+10) \\ 6(x+4)=(x+4)(x+10) \\ \text{divide both sides by (x+4)} \\ 6=x+10 \\ x=6-10 \\ x=-4 \end{gathered}[/tex]

The excluded value is x = - 4. The excluded value is the number that will make the denominator of the fraction equals to zero.