Question

if a =4/9 and b= 3/5, evaluate {(1/a)}+{(1/b)}x{(1/a+b)}​

Answer 1

Step-by-step explanation:

$value \: of \: a = \frac{4}{9} \\ value \: of \: b = \frac{3}{5} \\ therefore \: \frac{1}{a} + \frac{1}{b} \times \frac{1}{a +b } \\ = \frac{1}{ \frac{4}{9} } + \frac{1}{ \frac{3}{5} } \times \frac{1}{ \frac{4}{9} \times \frac{3}{5} }$

Now, we have to level both the numbers.

$\frac{4}{9} = \frac{4 \times 5}{9 \times 5} = \frac{20}{45} \\ and \\ \frac{3}{5} = \frac{3 \times 5}{5 \times 9} = \frac{15}{45}$

Now, Let's find the answer

$\frac{1}{ \frac{20}{45} } + \frac{1}{ \frac{15}{45} } + \frac{1}{ \frac{20}{45} \times \frac{15}{45} } \\ = \frac{1}{ \frac{35}{40} } + \frac{1}{ \frac{300}{2025} }$

Now, let's level those fractions

$\frac{35}{40} = \frac{7}{8} \\ and \\ \frac{300}{2025} = \frac{60}{405} \\ = \frac{60}{405} = \frac{15}{81}$

Now,

$\frac{7}{8} + \frac{15}{81} \\ = \frac{567}{648} + \frac{120}{648} \\ = \frac{567 + 120}{648} \\ = \frac{687}{648} \\ = \frac{229}{216} \\ = 1 \frac{13}{216}$

Hope it helped.

Answer 2

Answer:

Therefore=45/12 Or 3.75

Step-by-step explanation:

{(1/a)}+{(1/b)}x{(1/a+b)}

(1/4/9)+(1/3/5)×(1/4/9+3/5)

(9/4)+(5/3)×(1/20+27/45)

(9/4)+(5/3)×(45/47)

(27+20/12)×(45/4)

(47/45) ×(45/47)

45/12 OR 3.75