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# Algebra

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Given $$3x+\dfrac{2}{x}-4=2(x+2)-\left(9-\dfrac{1}{x}\right)$$ what is $$\dfrac{x^2+1}{x}?$$

Jun 24, 2022

#1
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Note that $${{x^2 + 1} \over x} = {x^2 \over x} + {1 \over x} = x + {1 \over x}$$

Now, simplify the equation to: $$3x + {2 \over x} - 4 = 2x -5+ {1 \over x}$$

Now, subtract $$2x$$ from both sides: $$x + {2 \over x} - 4 = -5 + {1 \over x}$$

Subtract $${1 \over x}$$ from both sides: $$x + {1 \over x} - 4 = -5$$

Can you take it from here?

Jun 24, 2022

#1
+2448
0

Note that $${{x^2 + 1} \over x} = {x^2 \over x} + {1 \over x} = x + {1 \over x}$$

Now, simplify the equation to: $$3x + {2 \over x} - 4 = 2x -5+ {1 \over x}$$

Now, subtract $$2x$$ from both sides: $$x + {2 \over x} - 4 = -5 + {1 \over x}$$

Subtract $${1 \over x}$$ from both sides: $$x + {1 \over x} - 4 = -5$$

Can you take it from here?

BuilderBoi Jun 24, 2022