Simplify 3root5 - 4root5 divided by 3root5 + 4root5
To simplify the expression (3√5 - 4√5) / (3√5 + 4√5), we can combine the terms that have the same radical.
Rewriting the expression, we get (3 - 4)√5 / (3 + 4)√5.
Simplifying further, we get -√5 / 7√5.
Since the radicals are the same, we can cancel them out, resulting in -1/7.
Therefore, (3√5 - 4√5) / (3√5 + 4√5) simplifies to -1/7.
To simplify the expression (3√5 - 4√5) / (3√5 + 4√5), we can use the conjugate. The conjugate of √5 is -√5.
Multiplying the numerator and denominator by the conjugate would help eliminate the radical in the denominator.
((3√5 - 4√5) / (3√5 + 4√5)) * ((-√5) / (-√5))
Simplifying the numerator:
3√5 - 4√5 = -√5
Simplifying the denominator:
(3√5 + 4√5) * (-√5) = (-15)
Now, the expression becomes:
-(√5) / (-15)
Since - divided by - is positive, we can rewrite the expression as:
√5 / 15
So, the simplified expression is √5 / 15.