Алгебра 9 класс учебник Макарычев, Миндюк ответы – номер 737

а) х/х – 3 – 5/х + 3 = $$\frac{18}{x^2 - 9}$$

$$\frac{x^2 - 2х + 15}{x^2 - 9}$$ = $$\frac{18}{x^2 - 9}$$

x² – 9 ≠ 0
x² ≠ 9
x ≠ 3; x ≠ –3
x² – 2x – 3 = 0
(x + 1)(x – 3) = 0
x₁ = –1; x₂ = 3
Ответ: –1

б) $$\frac{70}{x^2 - 16}$$ – 17/х – 4 = 3х/х + 4

$$\frac{3х^2 + 5х + 68}{x^2 - 16}$$ = $$\frac{70}{x^2 - 16}$$

x² – 16 ≠ 0
x² ≠ 16
x ≠ 4; x ≠ –4
3x² + 5x – 2 = 0
(x + 2)(x – 1/3) = 0
x₁ = –2; x₂ = 1/3
Ответ: –2; 1/3

в) $$\frac{3}{(2 - х)^2}$$ – $$\frac{5}{(х + 2)^2}$$ = $$\frac{14}{х^2 - 4}$$

$$\frac{-2х^2 + 32х - 8}{(х^2 - 4)^2}$$ = $$\frac{14}{х^2 - 4}$$

x² – 4 ≠ 0
x² ≠ 4
x ≠ 4; x ≠ –4
–2x² + 32z – 8 = 14(x² – 4)
x² – 2x – 3 = 0
x₁ = –1; x₂ = 3
Ответ: –1; 3

г) $$\frac{2}{4 - х^2}$$ – $$\frac{1}{2х - 4}$$ – $$\frac{7}{2х^2 + 4х}$$ = 0

$$\frac{х^2 + 13х - 14}{2х(2 - х)(2 + х)}$$ = 0

x² – 4 ≠ 0
x² ≠ 4
x ≠ 2; x ≠ –2
x² + 13x – 14 = 0
(x + 14)(x – 1) = 0
x₁ = –14; x₂ = 1
Ответ: –14; 1

д) $$\frac{1}{х^2 - 9}$$ + $$\frac{1}{3х - х^2}$$ = $$\frac{3}{2х + 6}$$

1/(х + 3)(х – 3) – 1/х(х + 3) = 3/2(х + 3) | · 2x(x + 3)(x – 3)

x ≠ – 3; x ≠ 3; x ≠ 0
2x – 2(x + 3) = 3x(x – 3)
2x – 2x – 6 = 3x² – 9
3x² – 9x + 6 = 0
x² – 3x + 2 = 0
По теореме Виета:
x₁ = 2; x₂ = 1
Ответ: x = 1; x = 2

е) $$\frac{2}{1 - х^2}$$ – $$\frac{1}{1 - х}$$ + $$\frac{4}{(х + 1)^2}$$ = 0

х ≠ –1, х ≠ 1
2(x + 1) – (x + 1)² + 4(1 – x) = 0
2x + 2 – (x² + 2x + 1) + 4 – 4x = 0
–x² – 4x + 5 = 0
x² + 4x – 5 = 0
По теореме Виета:
x₁ = 1; x₂ = –5
Ответ: 1; –5

ж) $$\frac{2}{х^2 + 5х}$$ + $$\frac{3}{2х - 10}$$ = $$\frac{15}{х^2 - 25}$$

2/х(х + 5) + 3/2(х – 5) = 15/(х – 5)(х + 5)
x ≠ 5; x ≠ –5; x ≠ 0
4(x – 5) + 3x(x + 5) = 30x
4x – 20 + 3x² + 15x – 30x = 0
3x² – 11x – 20 = 0
D = (–11)² – 4 · 3 · (–20) = 121 + 240 = 361
x = $$\frac{11 ± \sqrt{361}}{2 · 3}$$ = 11 ± 19/6
x₁ = 5; x₂ = –8/6 = –4/3 = –11/3
Ответ: x = –11/3

з) $$\frac{5}{2х + 6}$$ – $$\frac{1}{6х^2 - 18х}$$ = $$\frac{29}{27 - х^2}$$

$$\frac{5}{2(х + 3)}$$ – $$\frac{1}{6х(х - 3)}$$ = $$\frac{29}{3(9 - х^2)}$$

x ≠ –3; x ≠ 3; x ≠ 0
15x(3 – x) + (3 + x) = 29 · 2x
45x – 15x² + 3 + x – 58x = 0
5x² + 4x – 1 = 0
D = 4² – 4 · 5 · (–1) = 16 + 20 = 36
x = $$\frac{-4 ± \sqrt{36}}{2 · 5}$$ = –4 ± 6/10
X₁ = 0,2; x₂ = –1

и) х/х – 5 – 4/х + 5 + $$\frac{76}{25 - х^2}$$ = 0

х/х – 5 – 4/х + 5 – 76/(х – 5)(х + 5) = 0

x ≠ –5; x ≠ 5
x(x + 5) – 4(x – 5) – 76 = 0
x² + 5x – 4x + 20 – 76 = 0
x² + x – 56 = 0
По теореме Виета:
х₁ = 7; x₂ = –8

к) $$\frac{7х}{х^2 - 36}$$ + $$\frac{3}{6 - х}$$ = $$\frac{7}{х + 6}$$

7х/(х – 6)(х + 6) – 3/х + 6 = 7/х + 6

x ≠ –6; x ≠ 6
7x – 3(x + 6) = 7(x – 6)
7x – 3x – 18 – 7x + 42 = 0
–3x = –24
x = 8