Question

its says solve the euation allgebraically. Check for extraneous solutions. The equation is x + 2 = 15/x

Answer 1

If we multiply by x on both sides, we get a quadratic equation that we can either factor or use the quadratic formula on. So multiplying by x on both sides gives:
x^2 + 2 = 15
Then subtract by 15 on both sides to get it into a form we can factor or use the formula:
x^2 + 2 - 15 = 0.
It just so happens this one factors nicely:
x^2 + 2 - 15 = (x + 5)(x - 3) = 0
setting each factor equal to 0 gives the roots x = -5 and x = 3. Check that they do work by plugging this back into your original equation.

Answer 2

thank you so much!