реши 26 27 и 28
Analyzing polynomial factors
I’m examining the fraction involving \(n^4 - n^? - n^2\), and I think the exponent on the second \(n\) could be 3 based on what I see. The denominator appears to factor as \(n^4 - n^3 - n^2\), which simplifies nicely to \(1/n^2\). I'm making sure I have the right numerator, \(n^2 - n - 1\), and everything fits together. Since the instructions suggest minimal computations, I wonder if I need to note domain exclusions or if it’s enough to show the simplifications.Identifying fraction details
I need to tackle exercises 26, 27, and 28, starting with exercise 26. It seems the numerator might be \(b^2 + xy\) and the denominator \(x^2 + xy\). I'll take a closer look at the image to check if there’s any common factor, but it sounds like there isn't. Still, the exercise suggests factoring and canceling, which makes me wonder if the numerator is actually \(x^2 + xy\). That would simplify to 1, which feels odd. I might need to inspect the image more closely for clarity.Analyzing fractions
I'm working through a math problem involving fractions. I initially thought the numerator was \(b^2 + by\), but it might be \(y^2 + xy\), and the denominator is likely \(x^2 + xy\). I’m trying to confirm if there’s a common factor that simplifies this. I spot a possible misunderstanding with the variable symbols in a low-resolution image, where I confusingly read a lowercase \(b\) as an \(x\). This seems to suggest that I might need to simplify to \(y/x\).Simplifying fractions
I’m looking at a fraction, specifically \((y^2 + xy)/(x^2 + xy)\), and I believe it's meant to simplify to \(y/x\). I notice that in the image, the top part shows something that could be \(b^2 + xy\), but I think the first variable could actually be \(y\). Zooming in, it appears to confirm that the numerator is likely \(y^2 + xy\) and the denominator \(x^2 + xy\). Once I factor it out, it simplifies back to \(y/x\). I’ll make sure to use that!
26
а) \(\dfrac{x(a-b)}{x(m+n)}=\boxed{\dfrac{a-b}{m+n}}\)
б) \(\dfrac{a(m-n)}{b(m-n)}=\boxed{\dfrac ab}\)
в) \(\dfrac{x(x-2)}{y(x-2)}=\boxed{\dfrac xy}\)
г) \(\dfrac{d(d-1)}{d(d+1)}=\boxed{\dfrac{d-1}{d+1}}\)
д) \(\dfrac{a(a+b)}{a(a+c)}=\boxed{\dfrac{a+b}{a+c}}\)
е) \(\dfrac{y(x+y)}{x(x+y)}=\boxed{\dfrac yx}\)
27
а) \(\dfrac{y^3}{y^2(y+1)}=\boxed{\dfrac y{y+1}}\)
б) \(\dfrac{5a^2}{a^2(a^2+1)}=\boxed{\dfrac5{a^2+1}}\)
в) \(\dfrac{x^3(x^2+1)}{x^2+1}=\boxed{x^3}\)
г) \(\dfrac{b^4(b-1)}{b^5}=\boxed{\dfrac{b-1}{b}}\)
д) \(\dfrac{m^3(m-1)}{m^2(m+1)}=\boxed{\dfrac{m(m-1)}{m+1}}\)
е) \(\dfrac{n^2-n-1}{n^2(n^2-n-1)}=\boxed{\dfrac1{n^2}}\)
28
а) \(\dfrac{(x-3y)(x+3y)}{x+3y}=\boxed{x-3y}\)
б) \(\dfrac{a+2b}{(a+2b)^2}=\boxed{\dfrac1{a+2b}}\)
в) \(\dfrac{(m-n)(m+n)}{n(m-n)}=\boxed{\dfrac{m+n}{n}}\)
г) \(\dfrac{a(x-y)}{(x-y)^2}=\boxed{\dfrac a{x-y}}\)
д) \(\dfrac{2a(b-3)}{(b-3)^2}=\boxed{\dfrac{2a}{b-3}}\)
е) \(\dfrac{5n(n+2)}{(n-2)(n+2)}=\boxed{\dfrac{5n}{n-2}}\)
