Question

4m^2+3m*n-n^2/3m^2+4mn+n^2,если m/n=5/12

Answer 1

6-9n+6mn-4m

  3n2+n-2

 

(3(2-3n)-2m(2-3n))/((n+1)(3n-2))=((2-3n)(3-2m))/((n+1)(3n-2))=(2-3m)/(n+1)

Answer 2

To simplify the expression, we first need to substitute the given value of m/n into the expression. We are given that m/n = 5/12, which means we can rewrite m and n in terms of a single variable, say "k," such that m = 5k and n = 12k.

Now, let's substitute these values into the expression:

(4m^2 + 3mn - n^2) / (3m^2 + 4mn + n^2)

Substitute m and n:

(4(5k)^2 + 3(5k)(12k) - (12k)^2) / (3(5k)^2 + 4(5k)(12k) + (12k)^2)

Now simplify the expression:

(4 * 25k^2 + 3 * 60k^2 - 144k^2) / (3 * 25k^2 + 4 * 60k^2 + 144k^2)

(100k^2 + 180k^2 - 144k^2) / (75k^2 + 240k^2 + 144k^2)

(136k^2) / (459k^2)

Now we can simplify the expression further by canceling out common terms:

136 / 459

Thus, the simplified expression, when m/n = 5/12, is 136/459.