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

Question

18763 views around the world

You can reuse this answer
Creative Commons License

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!