Question

Решите номера на фотографии. С решением пожалуйста.

Answer 1

a)

$\frac{(a+1)^2+1}{a^4+4}\\\\\frac{a^2+2a+1+1}{a^4+4}\\\\\frac{a^2+2a+2}{a^4+4}$

б)

$\frac{b^3+1}{b^5+b^4+b^3+b^2+b+1}\\\\\frac{b^3+1}{b^3*(b^2+b+1)+b^2+b+1}\\\\\frac{b^3+1}{(b^2+b+b)*(b^3+1)}\\\\\frac{1}{b^2+b+1}$

в)

$\frac{9x^2+3x+1}{81x^4+9x^2+1}\\\\\frac{9x^2+3x+1}{81x^4-27x^3+27x^3+9x^2-9x^2+9x^2+3x-3x+1}\\\\\frac{9x^2+3x+1}{9x^2*(9x^2-3x+1)+3x*(9x^2-3x+1)+9x^2-3x+1}\\\\\frac{9x^2+3x+1}{(9x^2-3x+1)*(9x^2+3x+1)}\\\\\frac{1}{9x^2-3x+1}$

г)

$\frac{8y^6-1}{16y^8-4y^4-4y^2-1}\\\\\frac{8y^6}{4y^2*(4y^6-y^2-1)}\\\\\frac{2y^4}{4y^6-y^2-1}$

д)

$\frac{(x-4)^2+(x-8)^2-10}{(x+1)^2+(x-3)^2-80}\\\\\frac{x^2-8x+16+x^2-16x+64-10}{x^2+2x+1+x^2-6x+9-80}\\\\\frac{2x^2-24x+70}{2x^2-4x-70}\\\\\frac{2*(x^2-12x+35)}{2*(x^2-2x-35)}\\\\\frac{x^2-5x-7x+35}{x^2+5x-7x-35}\\\\\frac{x*(x-5)-7(x-5)}{x*(x+5)-7(x+5)}\\\\\frac{(x-5)*(x-7)}{(x+5)*(x-7)}\\\\\frac{x-5}{x+5}$

е)

$\frac{(ax-by)^2+(bx+ay)^2}{(cx-ay)^2+(ax+cy)^2}\\\\\frac{a^2x^2-2abxy+b^2y^2+b^2x^2+2abxy+a^2y^2}{c^2x^2-2acxy+a^2y^2+a^2x^2+2acxy+c^2y^2}\\\\\frac{x^2*(a^2+b^2)+y^2*(b^2+a^2)}{x^2*(c^2+a^2)+y^2*(a^2+c^2)}\\\\\frac{(a^2+b^2)*(x^2+y^2)}{(c^2+a^2)*(x^2+y^2)}\\\\\frac{a^2+b^2}{c^2+a^2}$

ж)

$\frac{2a^4+a^3+4a^2+a+2}{2a^3-a^2+a-2}\\\\\frac{2a^4+a^3+2a^2+2a^2+a+2}{2(a^3-1)-a*(a-1)}\\\\\frac{2a^2*9a^2+1)+a*(a^21)+2*(a^2+1)}{2*(a-1)*(a^2+a+1)-a*(a-1)}\\\\\frac{(a^2+1)*(2a^2+a+2)}{(a-1)*(2(a^2+a+1)-a)}\\\\\frac{(a^2+1)*(2a^2+a+2)}{(a-1)*(2a^2+2a+2-a)}\\\\\frac{(a^2+1)*(2a^2+a+2)}{(a-1)*(2a^2+a+2)}\\\\\frac{a^2+1}{a-1}$

з)

$\frac{a^3-2a^2+5a+26}{a^3-5a^2+17a-13}\\\\\frac{a^3+2a^2-4a^2-8a+13a+26}{a^3-a^2-4a^2+4a+13a-13}\\\\\frac{a^2*(a+2)-4a*(a+2)+13*(a+2)}{a^2*(a-1)-4a*(a-1)+13*(a-1)}\\\\\frac{(a+2)*(a^2-4a+13)}{(a-1)*(a^2-4a+13)}\\\\\frac{a+2}{a-1}$

вроде всё правильно