44. Упростите выражение: а) \(\frac{x^6+x^4}{x^4+x^2}\); б) \(\frac{y^6-y^8}{y^4-y^2}\); в) \(\frac{b^7-b^{10}}{b^5-b^2}\); г) \(\frac{c^6-c^4}{c^3-c^2}\).

а)

\[\frac{x^6+x^4}{x^4+x^2}=\frac{x^4(x^2+1)}{x^2(x^2+1)}=x^2,\quad x\ne0.\]

б)

\[\frac{y^6-y^8}{y^4-y^2}=\frac{y^6(1-y^2)}{y^2(y^2-1)}=-\frac{y^6(y^2-1)}{y^2(y^2-1)}=-y^4,\quad y\ne0,\ y\ne\pm1.\]

в)

\[\frac{b^7-b^{10}}{b^5-b^2}=\frac{b^7(1-b^3)}{b^2(b^3-1)}=-\frac{b^7(b^3-1)}{b^2(b^3-1)}=-b^5,\quad b\ne0,\ b^3\ne1.\]

г)

\[\frac{c^6-c^4}{c^3-c^2}=\frac{c^4(c^2-1)}{c^2(c-1)}=\frac{c^4(c-1)(c+1)}{c^2(c-1)}=c^2(c+1),\quad c\ne0,\ c\ne1.\]

Ответ: а) \(x^2\); б) \(-y^4\); в) \(-b^5\); г) \(c^2(c+1)\).