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Calculate the value
Answer
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$5n ^{ 2 } -11mn+6m ^{ 2 } \div m-n$
$- 11 m n + 6 m + 5 n ^ { 2 } - n$
Arrange the rational expression
$5 n ^ { 2 } - 11 m n + 6 m ^ { 2 } \div \color{#FF6800}{ m } - n$
$ $ If the exponent is omitted, the exponent of that term is equal to 1 $ $
$5 n ^ { 2 } - 11 m n + 6 m ^ { 2 } \div \color{#FF6800}{ m } ^ { \color{#FF6800}{ 1 } } - n$
$5 n ^ { 2 } - 11 m n + 6 m ^ { 2 } \div \color{#FF6800}{ m } ^ { \color{#FF6800}{ 1 } } - n$
$ $ Convert the division to multiplication and the exponent to the opposite symbol $ $
$5 n ^ { 2 } - 11 m n + 6 m ^ { 2 } \color{#FF6800}{ m } ^ { \color{#FF6800}{ - } \color{#FF6800}{ 1 } } - n$
$5 n ^ { 2 } - 11 m n + 6 \color{#FF6800}{ m } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ m } ^ { \color{#FF6800}{ - } \color{#FF6800}{ 1 } } - n$
$ $ Add the exponent as the base is the same $ $
$5 n ^ { 2 } - 11 m n + 6 \color{#FF6800}{ m } ^ { \color{#FF6800}{ 2 } \color{#FF6800}{ - } \color{#FF6800}{ 1 } } - n$
$5 n ^ { 2 } - 11 m n + 6 m ^ { \color{#FF6800}{ 2 } \color{#FF6800}{ - } \color{#FF6800}{ 1 } } - n$
$ $ Subtract $ 1 $ from $ 2$
$5 n ^ { 2 } - 11 m n + 6 m ^ { \color{#FF6800}{ 1 } } - n$
$5 n ^ { 2 } - 11 m n + 6 m ^ { \color{#FF6800}{ 1 } } - n$
$ $ If the exponent is 1, get rid of it as it is unnecessary $ $
$5 n ^ { 2 } - 11 m n + 6 m - n$
$\color{#FF6800}{ 5 } \color{#FF6800}{ n } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 11 } \color{#FF6800}{ m } \color{#FF6800}{ n } \color{#FF6800}{ + } \color{#FF6800}{ 6 } \color{#FF6800}{ m } \color{#FF6800}{ - } \color{#FF6800}{ n }$
$ $ Organize the expression $ $
$\color{#FF6800}{ - } \color{#FF6800}{ 11 } \color{#FF6800}{ m } \color{#FF6800}{ n } \color{#FF6800}{ + } \color{#FF6800}{ 6 } \color{#FF6800}{ m } \color{#FF6800}{ + } \color{#FF6800}{ 5 } \color{#FF6800}{ n } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ n }$
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