`Perform the indicated operations and simplify.
(z-1)/(z-8)-(z+1)/(z+8)+(z-120)/(z^2-64)
did you notice that
z^2 - 64 = (z+8)(z-8) , the other two denominators?
so z^2 - 64 is the common denominator, and
[(z-1)(z+8) - (z+1)(z-8) + z-120]/(z-64)
= [z^2 + 7z - 8 - (z^2 - 7z - 8) + z-120]/z^2-64)
= (15z - 120]/(z^2-64)
= 15(z-8)/(z^2-64)
= 15/(x+8) , z ≠ 8
Actually I kept t hinking the first two cancelled each other out because one was positive and the other negative. That's why I have been having such a hard time with this one. Thanks so much for your help.
Solve 6x^4-19x^2+10=0
I got
x=-0.816496581, 0.816496581
x=-1.58113883, 1.58113883
Is this correct? It just doesn't seem right to me.
I got the same answers
To simplify the expression, you need to find a common denominator for all the fractions. The common denominator in this case is (z^2 - 64), which is the difference of squares.
Let's break down the expression step by step:
1. (z - 1)/(z - 8) - (z + 1)/(z + 8) + (z - 120)/(z^2 - 64)
To add or subtract fractions, you need to have a common denominator. In this case, the common denominator is (z^2 - 64).
2. Simplify the first fraction: (z - 1)/(z - 8)
The numerator of this fraction is already in its simplest form. The denominator, however, can be factored into (z - 8) * (z + 8). Therefore, the first fraction can be rewritten as:
(z - 1)/[(z - 8) * (z + 8)]
3. Simplify the second fraction: (z + 1)/(z + 8)
Similar to the first fraction, the numerator is already in its simplest form. The denominator, (z + 8), does not need further simplification.
4. Simplify the third fraction: (z - 120)/(z^2 - 64)
The numerator of this fraction doesn't simplify further, but the denominator, (z^2 - 64), can be factored into (z - 8) * (z + 8). Therefore, the third fraction can be rewritten as:
(z - 120)/[(z - 8) * (z + 8)]
5. Now, we'll combine the fractions:
[(z - 1)/[(z - 8) * (z + 8)]] - [(z + 1)/(z + 8)] + [(z - 120)/[(z - 8) * (z + 8)]]
Since the denominators are the same for all the fractions, we can combine the numerators:
[(z - 1) - (z + 1) + (z - 120)] / [(z - 8) * (z + 8)]
6. Simplify the numerator: (z - 1) - (z + 1) + (z - 120)
Combining like terms, we have:
(z - z - z) + (-1 - 1 - 120) = -3z - 122
7. Rewrite the expression:
(-3z - 122) / [(z - 8) * (z + 8)]
And that's the simplified form of the expression.