Question

if x=(12mn)/(m+n) , find the value of (x+6m)/(x-6m)+(x+6n)/(x-6n) ........The answer is 2............ Please solve this , i will mark the correct answer with proper steps as the brainliest ...please help​

Answer 1

Given,

$\displaystyle\longrightarrow\sf{x=\dfrac {12mn}{m+n}}$

Then,

• $\displaystyle\sf{x+6m=\dfrac {12mn}{m+n}+6m}$

• $\displaystyle\sf{x+6m=\dfrac {12mn+6m(m+n)}{m+n}}$

• $\displaystyle\sf{x+6m=\dfrac {12mn+6m^2+6mn}{m+n}}$

• $\displaystyle\sf{x+6m=\dfrac {6m(m+3n)}{m+n}}$

And,

• $\displaystyle\sf{x-6m=\dfrac {12mn}{m+n}-6m}$

• $\displaystyle\sf{x-6m=\dfrac {12mn-6m(m+n)}{m+n}}$

• $\displaystyle\sf{x-6m=\dfrac {12mn-6m^2-6mn}{m+n}}$

• $\displaystyle\sf{x-6m=\dfrac {-6m(m-n)}{m+n}}$

And,

• $\displaystyle\sf{x+6n=\dfrac {12mn}{m+n}+6n}$

• $\displaystyle\sf{x+6n=\dfrac {12mn+6n(m+n)}{m+n}}$

• $\displaystyle\sf{x+6n=\dfrac {12mn+6mn+6n^2}{m+n}}$

• $\displaystyle\sf{x+6n=\dfrac {6n(3m+n)}{m+n}}$

And,

• $\displaystyle\sf{x-6n=\dfrac {12mn}{m+n}-6n}$

• $\displaystyle\sf{x-6n=\dfrac {12mn-6n(m+n)}{m+n}}$

• $\displaystyle\sf{x-6n=\dfrac {12mn-6mn-6n^2}{m+n}}$

• $\displaystyle\sf{x-6n=\dfrac {6n(m-n)}{m+n}}$

Thus,

$\displaystyle\longrightarrow\sf{\dfrac {x+6m}{x-6m}+\dfrac {x+6n}{x-6n}=\dfrac {\left (\dfrac {6m(m+3n)}{m+n}\right)}{\left (\dfrac {-6m(m-n)}{m+n}\right)}+\dfrac {\left (\dfrac {6n(3m+n)}{m+n}\right)}{\left (\dfrac {6n(m-n)}{m+n}\right)}}$

$\displaystyle\longrightarrow\sf{\dfrac {x+6m}{x-6m}+\dfrac {x+6n}{x-6n}=\dfrac {6m(m+3n)}{-6m(m-n)}+\dfrac {6n(3m+n)}{6n(m-n)}}$

$\displaystyle\longrightarrow\sf{\dfrac {x+6m}{x-6m}+\dfrac {x+6n}{x-6n}=\dfrac {3m+n}{m-n}-\dfrac {m+3n}{m-n}}$

$\displaystyle\longrightarrow\sf{\dfrac {x+6m}{x-6m}+\dfrac {x+6n}{x-6n}=\dfrac {3m+n-m-3n}{m-n}}$

$\displaystyle\longrightarrow\sf{\dfrac {x+6m}{x-6m}+\dfrac {x+6n}{x-6n}=\dfrac {2(m-n)}{m-n}}$

$\displaystyle\longrightarrow\sf{\underline {\underline {\dfrac {x+6m}{x-6m}+\dfrac {x+6n}{x-6n}=2}}}$

Answer 2

Answer:

Step-by-step explanation:

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C and D means Componendo and Dividendo