SOLUTION: equation with rational expressions solve x/x+1+6/x+7 , and please x-3/5=x-3/x

Question 306152: equation with rational expressions solve
x/x+1+6/x+7 , and please
x-3/5=x-3/x
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
[x/x+1] + [6/x+7]
---
gcd: (x+1)(x+7)
---
Rewrite both fraction with the gcd as its denominator:
---
[x(x+7)/gcd] + [6(x+1)/gcd]
---
Combine the numerators over the gcd:
---
[x^2+7x+6x+6]/gcd
---
[x^2+13x+6]/[(x^2+8x+7)
==============================
(x-3)/5 = (x-3)/x
---
Cross multiply to get:
x(x-3) = 5(x-3)
---
x^2-3x = 5x-15
x^2-8x+15 = 0
Factor:
(x-5)(x-3) = 0
x = 5 or x = 3
--------------------
Cheers,
Stan H.
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