19mm
If x= 12mn/m+ n find the value of X+ 6m/ x-6m+ X+6 n/ x-6m
Answers
Answer:
Given,
\displaystyle\longrightarrow\sf{x=\dfrac {12mn}{m+n}}⟶x=
m+n
12mn
Then,
\displaystyle\sf{x+6m=\dfrac {12mn}{m+n}+6m}x+6m=
m+n
12mn
+6m
\displaystyle\sf{x+6m=\dfrac {12mn+6m(m+n)}{m+n}}x+6m=
m+n
12mn+6m(m+n)
\displaystyle\sf{x+6m=\dfrac {12mn+6m^2+6mn}{m+n}}x+6m=
m+n
12mn+6m
2
+6mn
\displaystyle\sf{x+6m=\dfrac {6m(m+3n)}{m+n}}x+6m=
m+n
6m(m+3n)
And,
\displaystyle\sf{x-6m=\dfrac {12mn}{m+n}-6m}x−6m=
m+n
12mn
−6m
\displaystyle\sf{x-6m=\dfrac {12mn-6m(m+n)}{m+n}}x−6m=
m+n
12mn−6m(m+n)
\displaystyle\sf{x-6m=\dfrac {12mn-6m^2-6mn}{m+n}}x−6m=
m+n
12mn−6m
2
−6mn
\displaystyle\sf{x-6m=\dfrac {-6m(m-n)}{m+n}}x−6m=
m+n
−6m(m−n)
And,
\displaystyle\sf{x+6n=\dfrac {12mn}{m+n}+6n}x+6n=
m+n
12mn
+6n
\displaystyle\sf{x+6n=\dfrac {12mn+6n(m+n)}{m+n}}x+6n=
m+n
12mn+6n(m+n)
\displaystyle\sf{x+6n=\dfrac {12mn+6mn+6n^2}{m+n}}x+6n=
m+n
12mn+6mn+6n
2
\displaystyle\sf{x+6n=\dfrac {6n(3m+n)}{m+n}}x+6n=
m+n
6n(3m+n)
And,
\displaystyle\sf{x-6n=\dfrac {12mn}{m+n}-6n}x−6n=
m+n
12mn
−6n
\displaystyle\sf{x-6n=\dfrac {12mn-6n(m+n)}{m+n}}x−6n=
m+n
12mn−6n(m+n)
\displaystyle\sf{x-6n=\dfrac {12mn-6mn-6n^2}{m+n}}x−6n=
m+n
12mn−6mn−6n
2
\displaystyle\sf{x-6n=\dfrac {6n(m-n)}{m+n}}x−6n=
m+n
6n(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)}}⟶
x−6m
x+6m
+
x−6n
x+6n
=
(
m+n
−6m(m−n)
)
(
m+n
6m(m+3n)
)
+
(
m+n
6n(m−n)
)
(
m+n
6n(3m+n)
)
\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)}}⟶
x−6m
x+6m
+
x−6n
x+6n
=
−6m(m−n)
6m(m+3n)
+
6n(m−n)
6n(3m+n)
\displaystyle\longrightarrow\sf{\dfrac {x+6m}{x-6m}+\dfrac {x+6n}{x-6n}=\dfrac {3m+n}{m-n}-\dfrac {m+3n}{m-n}}⟶
x−6m
x+6m
+
x−6n
x+6n
=
m−n
3m+n
−
m−n
m+3n
\displaystyle\longrightarrow\sf{\dfrac {x+6m}{x-6m}+\dfrac {x+6n}{x-6n}=\dfrac {3m+n-m-3n}{m-n}}⟶
x−6m
x+6m
+
x−6n
x+6n
=
m−n
3m+n−m−3n
\displaystyle\longrightarrow\sf{\dfrac {x+6m}{x-6m}+\dfrac {x+6n}{x-6n}=\dfrac {2(m-n)}{m-n}}⟶
x−6m
x+6m
+
x−6n
x+6n
=
m−n
2(m−n)
\displaystyle\longrightarrow\sf{\underline {\underline {\dfrac {x+6m}{x-6m}+\dfrac {x+6n}{x-6n}=2}}}⟶
x−6m
x+6m
+
x−6n
x+6n
=2
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