Алгебра 9 класс учебник Макарычев, Миндюк ответы – номер 329

а) $$\frac{х^2 - 5х + 3}{х - 5}$$ – $$\frac{х^2 + 5х + 1}{х + 5}$$ = 1/4

х ≠ 5, х ≠ –5

$$\frac{х^2 - х}{х - 5}$$ + $$\frac{3}{х - 5}$$ – $$\frac{х^2 + 5х}{х + 5}$$ – $$\frac{1}{х + 5}$$ = 1/4

х(х – 5)/х – 5 – х(х + 5)/х + 5 + 3/х – 5 – 1/х + 5 = 1/4

х – х + 3/х – 5 – 1/х + 5 = 1/4

3/х – 5 – 1/х + 5 = 1/4

3 · 4(х + 5) – 1 · 4(х – 5) = 1 · (х + 5)(х – 5)
12х + 60 – 4х + 20 = х² – 25
х² – 8х – 105 = 0
D₁ = (–4)² – 1 · (–105) = 121

х = $$\frac{4 ± \sqrt{121}}{1}$$ = 4 ± 11

х₁ = 15, х₂ = –7

Ответ: 15 и –7

б) $$\frac{х^2 - 6х + 10}{х + 3}$$ – $$\frac{х^2 - 6х + 7}{х - 3}$$ = 71/8

х ≠ 3, х ≠ - 3

$$\frac{х^2 + 6х + 9}{х + 3}$$ + $$\frac{1}{х + 3}$$ – $$\frac{х^2 - 6х + 9}{х - 3}$$ + $$\frac{2}{х - 3}$$ = 57/8

$$\frac{(х + 3)^2}{х + 3}$$ – $$\frac{(х - 3)^2}{х - 3}$$ + 1/х + 3 + 2/х – 3 = 57/8

(х + 3) – (х – 3) + 1/х + 3 + 2/х – 3 = 57/8

х + 3 – х + 3 + 1/х + 3 + 2/х – 3 = 57/8

6 + 1/х + 3 + 2/х – 3 = 57/8

1/х + 3 + 2/х – 3 = 57/8 – 6

1/х + 3 + 2/х – 3 = 57 – 48/8

1/х + 3 + 2/х – 3 = 9/8

8(х – 3) + 2 · 8(х + 3) = 9(х + 3)(х – 3)
8х – 24 + 16х + 48 = 9х² – 81
24х + 24 = 9х² – 81
9х² – 24х – 81 – 24 = 0
9х² – 24х – 105 = 0
3х² – 8х – 35 = 0
D₁ = (–4)² – 3 · (–35) = 16 + 105 = 121

х = $$\frac{4 ± \sqrt{121}}{3}$$ = 4 ± 11/3

х₁ = 5, х₂ = –7/3 = –21/3

Ответ: 5 и –21/3