How do you solve 1/(x+3)+1/(x+5)=1?

1 Answer
Mar 21, 2016

Resolving this gives: "x^2+6x+7=0

I will let you finish that off (you need to use the formula).

Explanation:

The bottom number/expression (denominator) need to be the same to enable direct addition.

Multiply by 1 and you do not change the value. Multiply by 1 but in the form of 1=(x+5)/(x+5) you do not change the value but you do change the way it looks.

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Multiply 1/(x+3) by 1 but in the form of 1=(x+5)/(x+5)

Giving color(brown)(1/(x+3)xx(x+5)/(x+5) = (x+5)/((x+3)(x+5)))

Multiply 1/(x+5) by 1 but in the form of 1=(x+3)/(x+3)

Giving color(brown)(1/(x+5)xx(x+3)/(x+3) = (x+3)/((x+3)(x+5)))

color(blue)("Putting it all together")

" "(x+5)/((x+3)(x+5)) + (x+3)/((x+3)(x+5))=1

" "(2x+8)/((x+3)(x+5))=1

Multiply both sides by (x+3)(x+5) giving

" "(2x+8)xx(cancel((x+3)(x+5)))/(cancel((x+3)(x+5)))=1xx(x+3)(x+5)

" "2x+8=x^2+8x+15

" "x^2+6x+7=0

Use the formula to solve for x

I will let you do that

y=ax^2+bx+c" " where " "x=(-b+-sqrt(b^2-4ac))/(2a)
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Tony B