How do you solve $x+ 1/x = 10/3$ ?

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Answer 1 · 2016-05-17T00:38:16

Put on a common denominator

$(x xx x xx 3)/(3x) + (1 xx 3)/(3x) = (10 xx x)/3$

Multiply and then you can clear the denominators and solve like a regular quadratic equation.

$3x^2 + 3 = 10x$

$3x^2 - 10x + 3 = 0$

$3x^2 - 9x - x + 3 = 0$

$3x(x - 3) - 1(x - 3) = 0$

$(3x - 1)(x - 3) = 0$

$x = 1/3 and 3$

With rational equations, it's also important to note the restrictions on the variable.

There will be restrictions when the denominator is equal to 0, since in math division by 0 is undefined.

Therefore, $x!=0$

To summarize, $x = 1/3 and 3, x!=0$

Hopefully this helps!

How do you solve x+ 1/x = 10/3x+ 1/x = 10/3?