I have a couple of math questions that i cant seem to get to work out. can someone help me please.?
1.)
(x/x+6)-(6/x-6)=(x^2+36)/(x^2-36)
2.)
(r-2)-(2-r)=0
3.) add
(8/ty^2)+(9/t^2y)
4.)add
(7/w)+(8/w^2)
5.)add
((r+10)/r)+(r/(r+10))
6.) divide
((z^2-1)/16z+16) / ((z-1)/4)
7.) find LCM
11(t-7) and 77(t-7)
8.) remove factors of 1
w^2-9 / 3-w
9.) divide and simplify
((d+2)/(d-4))/((8d+16)/(d-5))
I know that there are alot of questions but these are the one's that for some reason i just cant get to work out.
Of course, I'd be happy to help you with your math questions! Let's go through each question one by one and I'll explain how to solve them.
1.) To solve the equation (x/x+6) - (6/x-6) = (x^2+36)/(x^2-36), we need to find a common denominator for the fractions. In this case, the common denominator is (x+6)(x-6).
Multiply each term in the equation by the common denominator to eliminate the fractions. After simplifying the expression, you should have: x(x-6) - 6(x+6) = x^2 + 36.
Expand and simplify both sides of the equation. Gather like terms and solve for x. The final answer should be x = 6.
2.) To solve the equation (r-2) - (2-r) = 0, we need to simplify the expression within the parentheses first. Distribute the negative sign through the second parentheses to get r - 2 - 2 + r = 0.
Combine like terms and simplify the equation to 2r - 4 = 0. Then, add 4 to both sides and divide by 2 to solve for r. The final answer should be r = 2.
3.) To add (8/ty^2) + (9/t^2y), find a common denominator for the fractions, which is t^2y^2. Multiply each term by the necessary factors to obtain the common denominator.
After simplifying the expression, you should have (8t + 9y)/t^2y^2 as the final answer.
4.) To add (7/w) + (8/w^2), find a common denominator for the fractions, which is w^2. Multiply each term by the necessary factors to obtain the common denominator.
After simplifying the expression, you should have (7w + 8)/w^2 as the final answer.
5.) To add ((r+10)/r) + (r/(r+10)), first find a common denominator for the fractions, which is r(r+10). Multiply each term by the necessary factors to obtain the common denominator.
After simplifying the expression, you should have (r^2 + 10r + r^2 + 10r)/(r(r+10)) as the final answer.
Combine like terms in the numerator and simplify, which gives you (2r^2 + 20r)/(r(r+10)) as the final answer.
6.) To divide ((z^2-1)/16z+16) by ((z-1)/4), remember that dividing by a fraction is the same as multiplying by its reciprocal.
Rewrite the division as a multiplication problem: ((z^2-1)/16z+16) * (4/(z-1)).
Next, simplify the expression by canceling out common factors in the numerator and denominator. This should give you (z+1)/(4z+4) as the final answer.
7.) To find the least common multiple (LCM) between 11(t-7) and 77(t-7), cancel out any common factors.
There is a common factor of (t-7) in both terms. Divide both terms by (t-7) to get 11 and 77.
To find the LCM, multiply the two terms (11 * 77). The LCM of 11(t-7) and 77(t-7) is 847(t-7).
8.) To remove factors of 1 from (w^2-9)/(3-w), factor the numerator and denominator.
The numerator can be factored as (w+3)(w-3) and the denominator can be factored as -(w-3).
Cancel out the common factors of (w-3) and simplify the expression. The final answer should be -(w+3)/(3-w).
9.) To divide and simplify ((d+2)/(d-4))/((8d+16)/(d-5)), remember that dividing by a fraction is the same as multiplying by its reciprocal.
Rewrite the division as a multiplication problem and simplify each fraction individually: ((d+2)/(d-4)) * ((d-5)/(8d+16)).
Combine like terms and simplify the expression further. The final answer should be (d+2)/(8d+16).