Simplify. 3root5 - 4root5/3root5 + 4root5
To simplify the expression, we can combine like terms by adding the terms that have the same radical.
(3√5 - 4√5)/(3√5 + 4√5)
Simplifying the numerator gives:
(-√5)/(3√5 + 4√5)
We can factor out √5 from the denominator:
(-√5)/(7√5)
Finally, we can cancel out the common factor of √5:
-1/7
To simplify the expression 3√5 - 4√5 / 3√5 + 4√5, we can combine the like terms.
First, let's look at the numerator: 3√5 - 4√5.
Since both terms have the same radical (√5), we can combine them by subtracting their coefficients: 3 - 4 = -1.
Therefore, the numerator simplifies to -√5.
Now let's simplify the denominator: 3√5 + 4√5.
Again, both terms have the same radical (√5), so we can combine them by adding their coefficients: 3 + 4 = 7.
Therefore, the denominator simplifies to 7√5.
Finally, we can rewrite the expression as: -√5 / 7√5.
However, we notice that the radical terms in the numerator and denominator cancel each other out.
Therefore, the simplified expression is -1 / 7.