How do you solve (1/x)+1/(x+3)=1/4 using the quadratic formula?

1 Answer
Tony B
May 3, 2016

color(blue)(x=6.772" and" -1.772)

Explanation:

Consider the left side

Common denominator is x(x+3)

So we have:

((x+3)+x)/(x(x+3))=1/4

(2x+3)/(x^2+3x)=1/4

Multiply both sides by (x^2+3x)

(2x+3)xx(x^2+3x)/(x^2+3x)=(x^2+3x)/4

but (x^2+3x)/(x^2+3x)=1

(2x+3)=(x^2+3x)/4

Multiply both sides by 4

4(2x+3)=x^2+3x

8x+12=x^2+3x

Subtract 8x and 12 from both sides

x^2+3x-8x-12=0

color(brown)(x^2-5x-12=0)
color(brown)("Now we can use the formula")
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Standard form y=ax^2+bx+c
where a=1" ; "b=-5" ; "c=-12

x=(-b+-sqrt(b^2-4ac))/(2a)

x=(5+-sqrt((-5)^2-4(1)(-12)))/(2(1))

x=(5+-sqrt(25+48))/2

x=(5+-sqrt(73))/2" " Note that 73 is a prime number

color(blue)(x=6.772" and" -1.772)

Tony B

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