Question

(Simplify): (m + b)/(m - b) + (m - b)/(m + b) - (m ^ 2 + b ^ 2)/(m ^ 2 - b ^ 2)​

Answer 1

Answer: To simplify the expression (m + b)/(m - b) + (m - b)/(m + b) - (m ^ 2 + b ^ 2)/(m ^ 2 - b ^ 2), we can first find a common denominator for the first two fractions, which is (m - b)(m + b), and then add them together. This gives us ((m + b) ^ 2 + (m - b) ^ 2) / (m ^ 2 - b ^ 2). We can then subtract the third fraction by finding a common denominator of (m - b)(m + b), which gives us (m ^ 2 + b ^ 2 - (m ^ 2 + b ^ 2)) / (m ^ 2 - b ^ 2). This simplifies to 0, so the final answer is just ((m + b) ^ 2 + (m - b) ^ 2) / (m ^ 2 - b ^ 2).

Answer 2

`\textsf{Simplified form is} \sf (m^2+b^2)/((m+b)(m-b)) \:\: or \:\: \sf (m^2+b^2)/((m+b)^2)`

Explanation:

`\sf ((m + b))/((m - b) )+( (m - b))/((m + b) )-( (m ^ 2 + b ^ 2))/((m ^ 2 - b ^ 2))`

Let's simply it.

We can factorize.

`\sf m^2-b^2 = (m+a)(m-a)`

Above expression can be written as:

`\sf ((m + b))/((m - b) )+( (m - b))/((m + b) )-( (m ^ 2 + b ^ 2))/((m+b)(m-b))`

Taking LCM (m+a)(m-a) from each:

we get

`\sf ((m+b)(m+b) +(m-b)(m-b) -(m^2+b^2))/((m+b)(m-b))`

Expand all

`\sf (m^2 +2mb+b^2 +m^2-2mb+b^2 -m^2-b^2)/((m+b)(m-b))`

Solving like terms

`\sf (m^2+b^2)/((m+b)(m-b))`

Therefore,

`\textsf{Simplified form is} \sf (m^2+b^2)/((m+b)(m-b)) \:\: or \:\: \sf (m^2+b^2)/((m+b)^2)`

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