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# The operation is defined for non-zero a andb as follows: If a+b=13 and , what is the value of ​?Express

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The operation $$*$$ is defined for non-zero a andb  as follows: $$a * b = \frac{1}{a} + \frac{1}{b}.$$  If a+b=13 and $$a \times b=25$$ , what is the value of $$a*b$$?Express your answer as a common fraction.

ant101  Aug 28, 2018

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We know that: $$\frac{1}{a}+\frac{1}{b}=a*b$$ . If we multiply the denominator by b and a, respectively, we get: $$\frac{1b}{ab}+\frac{1a}{ba}=a*b$$ . Suddenly, we go back to the problem, and it says: $$ab=25.$$ So, we have:$$\frac{1a}{25}+\frac{1b}{25}=\frac{1a+1b}{25}.$$ We also know that $$a+b=13$$ , so  $$\frac{1a+1b}{25}=\frac{a+b}{25}=\boxed{\frac{13}{25}}.$$

tertre  Aug 28, 2018
#1
+3270
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We know that: $$\frac{1}{a}+\frac{1}{b}=a*b$$ . If we multiply the denominator by b and a, respectively, we get: $$\frac{1b}{ab}+\frac{1a}{ba}=a*b$$ . Suddenly, we go back to the problem, and it says: $$ab=25.$$ So, we have:$$\frac{1a}{25}+\frac{1b}{25}=\frac{1a+1b}{25}.$$ We also know that $$a+b=13$$ , so  $$\frac{1a+1b}{25}=\frac{a+b}{25}=\boxed{\frac{13}{25}}.$$

tertre  Aug 28, 2018
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The operation $$*$$ is defined for non-zero a andb  as follows:

$$a * b = \frac{1}{a} + \frac{1}{b}.$$

If $$a+b=13$$ and $$a \times b=25$$

what is the value of  $$a*b$$  ?

Express your answer as a common fraction.

$$\begin{array}{|rcll|} \hline a+b &=& 13 \\ a\times b &=& 25 \\\\ \dfrac{a+b}{a\times b}&=& \dfrac{13}{25} \\\\ \dfrac{a}{a\times b} + \dfrac{b}{a\times b} &=& \dfrac{13}{25} \\\\ \dfrac{1}{b} + \dfrac{1}{a} &=& \dfrac{13}{25} \\\\ \dfrac{1}{a} + \dfrac{1}{b} &=& \dfrac{13}{25} \quad & | \quad \dfrac{1}{a} + \dfrac{1}{b} = a*b \\\\ \mathbf{a*b} & \mathbf{=} & \mathbf{\dfrac{13}{25}} \\ \hline \end{array}$$

heureka  Aug 28, 2018