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lana66690 [7]
3 years ago
7

6/a - 4/b = 1 and 9/a - 8/b = 1​

Mathematics
1 answer:
Alja [10]3 years ago
5 0

Answer:

a = 3 ; b = 4

Step-by-step explanation:

Eqn.1 = \frac{6}{a}  -  \frac{4}{b}  = 1

Eqn.2 = \frac{9}{a}  -  \frac{8}{b}  = 1

Both the eqns have RHS (Right Hand Side) equal. So,

\frac{6}{a}  -  \frac{4}{b}  =  \frac{9}{a}  -  \frac{8}{b}

=  >  \frac{6b - 4a}{ab}  =  \frac{9b - 8a}{ab}

Cancelling ab from both the denominators of both the sides,

=  > 6b - 4a = 9b - 8a

=  > 8a - 4a = 9b - 6b

=  > 4a = 3b

=  > a =  \frac{3b}{4}

Putting the value of a in Eqn.1,

\frac{6}{ \frac{3b}{4} }  -  \frac{4}{b}  = 1

=  >  \frac{24}{3b}  -  \frac{4}{b}  = 1

=  >  \frac{8}{b} -  \frac{4}{b}   = 1

=  >  \frac{8 - 4}{b}  = 1

=  > b = 4

Putting the value of b in the value of a

a =  \frac{3 \times 4}{4}  = 3

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