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Not sure how to simplify : (1 - (a+b)/(a-b))*(a^2-b^2)/(8b)
- Thread starter Zulgok
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bluedevil314
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- Oct 19, 2015
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Hello, how could I simplify this (1 - (a+b)/(a-b))*(a^2-b^2)/(8b) ? Answer is supposed to be (-a-b)/(4). Thank you in advance.
There is some factoring and cancellation involved. Let's focus on the last part of the numerator first: (a^2 - b^2) can be factored as (a+b)(a-b). When you multiply that by (1 - (a+b)/(a-b)), then you get (a^2 - b^2 - (a+b)(a+b)) because the (a-b)'s cancel each other out. FOIL out the second part (don't forget the minus sign) and you get (a^2 - b^2 - a^2 - 2ab - b^2), which is equivalent to (-2b^2 - 2ab). Now, factor out 2b and include the original denominator and you get 2b(-b - a)/8b. The b's cancel each other out, and 2*4 = 8, so you get the final answer of (-b-a)/4 or (-a-b)/4.
I hope that helps.
How far have you gotten? What have you tried? Please show us all of your work, even if you know it's wrong. If you're completely stuck and don't even know where to begin, a good first step is: Try finding a common denominator for the subtraction. Remember that you can rewrite 1 as anything, as long as the numerator and denominator are the same.
Did I do anything wrong in this one ?
((m+x)/(m-x)-(m^2)/(m^2-x^2))*(m-x)/(2m+x)
First I guess I have to do the first part before multiplying ? If so, then
((m+x)/(m-x)-(m^2)/(m^2-x^2)=(m^2+x^2-m^2)/(m-x)(m+x)=(x^2)/(m-x)(m+x).
Then (x^2)/((m-x)(m+x))*(m-x)/(2m+x)=(x^2)/(2m+x)(m+x)=(x^2)/(2m^2+3mx+x^2).
I was supposed to get (x)/(m+x). What did I do wrong ? Thank you.
((m+x)/(m-x)-(m^2)/(m^2-x^2))*(m-x)/(2m+x)
First I guess I have to do the first part before multiplying ? If so, then
((m+x)/(m-x)-(m^2)/(m^2-x^2)=(m^2+x^2-m^2)/(m-x)(m+x)=(x^2)/(m-x)(m+x).
Then (x^2)/((m-x)(m+x))*(m-x)/(2m+x)=(x^2)/(2m+x)(m+x)=(x^2)/(2m^2+3mx+x^2).
I was supposed to get (x)/(m+x). What did I do wrong ? Thank you.
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For the problem with m and x, it looks like you messed up when expanding a squared term. After creating a common denominator, this should be your subtraction problem.
\(\displaystyle \frac{m+x}{m-x}-\frac{m^2}{m^2-x^2}=\frac{\left(m+x\right)^2}{\left(m-x\right)\left(m+x\right)}-\frac{m^2}{\left(m-x\right)\left(m+x\right)}\)
Hint: \(\displaystyle \left(m+x\right)^2\ne m^2+x^2\)
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As for a2 - b2 = (a+b)(a-b), you can think of it kind of like a quadratic, where b is like the constant term. For instance, if we had:
x2 - 9 = x2 + 0x - 9 = (x+?)(x+?)
To factor this quadratic, we need to find two numbers which multiply to 9, and add to 0. So, 3 and -3 will work. Thus we have (x+3)(x-3). Similarly:
a2 - b2 = a2 + 0a - b^2 = (a+?)(a+?)
Here, we need two numbers which multiply to b2, and add to 0. The only way two numbers can add to zero is if they're negatives of each other, so then we know:
a2 - b2 = (a+b)(a-b)
\(\displaystyle \frac{m+x}{m-x}-\frac{m^2}{m^2-x^2}=\frac{\left(m+x\right)^2}{\left(m-x\right)\left(m+x\right)}-\frac{m^2}{\left(m-x\right)\left(m+x\right)}\)
Hint: \(\displaystyle \left(m+x\right)^2\ne m^2+x^2\)
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As for a2 - b2 = (a+b)(a-b), you can think of it kind of like a quadratic, where b is like the constant term. For instance, if we had:
x2 - 9 = x2 + 0x - 9 = (x+?)(x+?)
To factor this quadratic, we need to find two numbers which multiply to 9, and add to 0. So, 3 and -3 will work. Thus we have (x+3)(x-3). Similarly:
a2 - b2 = a2 + 0a - b^2 = (a+?)(a+?)
Here, we need two numbers which multiply to b2, and add to 0. The only way two numbers can add to zero is if they're negatives of each other, so then we know:
a2 - b2 = (a+b)(a-b)
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Thank you for your answer. I still cant seem to get the correct answer : (x)/(m+x);
((m+x)^2-m^2)/(m-x)(m+x)*(m-x)/(2m+x).
I could only remove those two, I couldnt find anything else. I also tried expanding a square, which was also able to simplify a bit :
(m+x)^2-m^2=m^2+2mx+x^2-m^2=2mx+x^2
((m+x)^2-m^2)/(m-x)(m+x)*(m-x)/(2m+x).
I could only remove those two, I couldnt find anything else. I also tried expanding a square, which was also able to simplify a bit :
(m+x)^2-m^2=m^2+2mx+x^2-m^2=2mx+x^2
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So, if I'm understanding correctly, this is where you are stuck:
\(\displaystyle \frac{2mx+x^2}{\left(m+x\right)\left(2m+x\right)}\)
Look carefully at the numerator. Are there any common terms you can factor out? What are you left with when you do? Then can you cancel any terms?
\(\displaystyle \frac{2mx+x^2}{\left(m+x\right)\left(2m+x\right)}\)
Look carefully at the numerator. Are there any common terms you can factor out? What are you left with when you do? Then can you cancel any terms?