SOLUTION: solve the equation by the method of your choice. 1 1 = 1 --- + -- ---- x+3 x 10

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Question 106852: solve the equation by the method of your choice.
1 1 = 1
--- + -- ----
x+3 x 10
Found 2 solutions by checkley75, Fombitz:
Answer by checkley75(3666) About Me  (Show Source):
You can put this solution on YOUR website!
1/(x+3)+1/x=1/10 find a common denominator for the left side fractions.
(x+x+3)/x(x+3)=1/10
(2x+3)/(x^2+3x)=1/10 now cross multiply
10(2x+3)=x^2+3x
20x+30=x^2+3x
x^2+3x-20x-30=0
x^2-17x-30=0
solve using the quadratic equation:
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
X=(17+-SQRT[-17^2-4*1*-30])/2*1
X=(17+-SQRT[289+120])/2
X=(17+-SQRT409)/2
X=(17+-20.22)/2
X=(17+20.22)/2
X=37.22/2
X=18.61 ANSWER.
X=(17-20.22)/2
X=-3.22/2
X=-1.61 ANSWER.

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
1%2F%28x%2B3%29%2B1%2Fx=1%2F10
First off, multiply both sides by the product of the denominators to get rid of the fractions.
P=10x%28x%2B3%29
10x%28x%2B3%29%2A%281%2F%28x%2B3%29%2B1%2Fx%29=10x%28x%2B3%29%2A%281%2F10%29Multiply by P.
10x%28x%2B3%29%2A%281%2F%28x%2B3%29%29%2B10x%28x%2B3%29%2A%281%2Fx%29=x%28x%2B3%29Distributive property.
10x%2B10%28x%2B3%29=x%28x%2B3%29
10x%2B10x%2B30=x%5E2%2B3x%29
20x%2B30=x%5E2%2B3x%29
x%5E2%2B3x-20x-30=0%29
x%5E2-17x-30=0%29Re-arrange all terms to form a quadratic equation.
x+=+%28-%28-17%29+%2B-+sqrt%28+%28-17%29%5E2-4%2A1%2A%28-30%29+%29%29%2F%282%2A1%29+ Quadratic formula.
x+=+%2817+%2B-+sqrt%28+289%2B120+%29%29%2F%282%29+
x+=+%2817+%2B-+sqrt%28+409+%29%29%2F%282%29+
x~(-1.612) or x~18.612
Check your answers.
%2818.612%2B3%29%5E%28-1%29%2B%2818.612%5E%28-1%29%29=1%2F10
%28.04627%29%2B%280.05372%29=1%2F10
.09999=0.10
Good answer.