If a = $\frac{7}{2}$ and b = $-\frac{5}{4}$
Find $\frac{a\ +\ b}{a\ -\ b}$.

Given: a = $\frac{7}{2}$ and b = $-\frac{5}{4}$

To find: Here we have to find the value of $\frac{a\ +\ b}{a\ -\ b}$, if a = $\frac{7}{2}$ and b = $-\frac{5}{4}$.

Solution:

a = $\frac{7}{2}$ and b = $-\frac{5}{4}$

Now,

$a\ +\ b\ =\ \frac{7}{2} \ +\ \left( -\ \frac{5}{4}\right)$

$a\ +\ b\ =\ \frac{7}{2} \ -\ \frac{5}{4}$

$a\ +\ b\ =\ \frac{14\ -\ 5}{4}$

$a\ +\ b\ =\ \mathbf{\frac{9}{4}}$

Also,

$a\ -\ b\ =\ \frac{7}{2} \ -\ \left( -\ \frac{5}{4}\right)$

$a\ -\ b\ =\ \frac{7}{2} \ +\ \frac{5}{4}$

$a\ -\ b\ =\ \frac{14\ +\ 5}{4}$

$a\ -\ b\ =\ \mathbf{\frac{19}{4}}$

So,

$\frac{a\ +\ b}{a\ -\ b}$

$=\ \frac{\frac{9}{4}}{\frac{19}{4}}$

$=\ \frac{9}{4} \ \times \ \frac{4}{19}$

$=\ \mathbf{\frac{9}{19}}$

So, value of $\frac{a\ +\ b}{a\ -\ b}$, if a = $\frac{7}{2}$ and b = $-\frac{5}{4}$ is $\frac{9}{19}$.

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Updated on: 10-Oct-2022

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