1)Can z+6/z+1 be reduced any further?
2)Add and simplify
v/v^2+8v+16 + 4/v^2+7v+12
3)For this second binomial do you change the the sign of the second term?
Subtract and simplify
1-y/y-2 - 9y-8/2-y
4)Solve
4/5+1/2=1/x
5)8/x=9/x-1/2
Thanks!
Unless you use parentheses, I can not tell what is the numerator and what is the denominator in your fractions.
1) To determine if the expression z+6/z+1 can be reduced further, we need to check if there are any common factors in the numerator and denominator. In this case, there are no common factors that can be simplified. Therefore, z+6/z+1 cannot be reduced any further.
2) To add and simplify the expression v/v^2+8v+16 + 4/v^2+7v+12, we first need to factor the denominators and find their least common multiple (LCM).
The denominators can be factored as follows:
v^2+8v+16 = (v+4)(v+4)
v^2+7v+12 = (v+3)(v+4)
The LCM is then (v+4)(v+3).
Now, we need to rewrite the fractions with the appropriate common denominator:
v/v^2+8v+16 = v/(v+4)(v+4) * (v+3)/(v+3) = (v(v+3))/[(v+4)(v+3)(v+4)]
4/v^2+7v+12 = 4/(v+3)(v+4)
Now, the expression becomes (v(v+3))/[(v+4)(v+3)(v+4)] + 4/(v+3)(v+4)
We can add the fractions by finding a common denominator:
(v(v+3) + 4)/[(v+4)(v+3)(v+4)]
Simplifying further, we get (v^2+3v+4)/[(v+4)(v+3)(v+4)]
3) To subtract and simplify the expression 1-y/y-2 - 9y-8/2-y, we need to make sure we have a common denominator.
For the first term, 1-y/y-2, we can multiply the numerator and denominator by -1 to change the sign of the fraction: (-1+y)/(2-y)
For the second term, 9y-8/2-y, we can rewrite as (-8+9y)/(2-y)
Now, the expression becomes (-1+y)/(2-y) - (-8+9y)/(2-y)
As the denominators are the same, we can combine the numerators: (-1+y-(-8+9y))/(2-y)
Simplifying further, we get (8y+7)/(2-y).
4) To solve the equation 4/5+1/2=1/x, we first need to find a common denominator for the fractions on the left side of the equation.
The common denominator is 10. Rewriting the fractions with this denominator, we get 8/10 + 5/10 = 1/x.
Simplifying, we have 13/10 = 1/x.
To solve for x, we can cross multiply: 13x = 10.
Dividing both sides by 13, x = 10/13.
5) To solve the equation 8/x = 9/x - 1/2, we first need to find a common denominator for the fractions involved. In this case, the common denominator is 2x.
Rewriting the equation with this denominator, we get 16/2x = 18/2x - x/2x.
Simplifying, we have 16/2x = (18 - x)/2x.
Now, we can cross multiply: 16 * 2x = (18 - x) * 2x.
Expanding both sides, we get 32x = 36x - x^2.
Rearranging the terms, we have x^2 = 4x.
Now, we can set the equation equal to zero: x^2 - 4x = 0.
Factoring out an x, we have x(x - 4) = 0.
So, the solutions are x = 0 and x = 4.