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222-9+11+12:2*14+14 = ? ( )

Toán Lớp 8: a) 3x+10/x+3+x+4/3-x b) 3x+5/x^2-5x+25-x/25-5x

Tháng Mười 5, 2022 Toán học 2 Comments 0 views

Toán Lớp 8: a) 3x+10/x+3+x+4/3-x b) 3x+5/x^2-5x+25-x/25-5x

Comments ( 2 )

  1. thienthanh
    thienthanh
    5 Tháng Mười, 2022 at 6:56 sáng
    Reply
    a) (3x+10)/(x+3)+(x+4)/(3-x) (x ne +-3)
    = (3x+10)/(x+3)-(x+4)/(x-3)  
    =((3x+10)(x-3)-(x+4)(x+3))/((x-3)(x+3))
    =(3x^2-9x+10x-30-x^2-3x-4x-12)/((x-3)(x+3)
    =(2x^2-6x-42)/((x-3)(x+3))
    b) (3x+5)/(x^2-5x)+(25-x)/(25-5x)(x ne 5)
    =(3x+5)/(x(x-5))+(x-25)/(5(x-5))
    =(5(3x+5)+x(x-25))/(5x(x-5))
    =(15x+25+x^2-25x)/(5x(x-5))
    =(x^2-10x+25)/(5x(x-5))
    =(x-5)^2/(5x(x-5))
    =(x-5)/(5x)

  2. trucoanh55
    trucoanh55
    5 Tháng Mười, 2022 at 6:56 sáng
    Reply
    Giải đáp:
    a) {2x^2 – 6x – 42}/{x^2 – 9}
    b) {x – 5}/{5x}
    Lời giải và giải thích chi tiết:
    a)
    {3x + 10}/{x + 3} + {x + 4}/{3 – x}       (ĐKXĐ: x ne +- 3)
    = {3x + 10}/{x + 3} + {x + 4}/{- (x – 3)}
    = {3x + 10}/{x + 3} – {x + 4}/{x – 3}
    = {(3x + 10)(x – 3)}/{(x – 3)(x + 3)} – {(x + 4)(x + 3)}/{(x – 3)(x + 3)}
    = {3x^2 – 9x + 10x – 30}/{(x – 3)(x + 3)} – {x^2 + 3x + 4x + 12}/{(x – 3)(x + 3)}
    = {3x^2 + x – 30}/{(x – 3)(x + 3)} – {x^2 + 7x + 12}/{(x – 3)(x + 3)}
    = {3x^2 + x – 30 – (x^2 + 7x + 12)}/{(x – 3)(x + 3)}
    = {3x^2 + x – 30 – x^2 – 7x – 12}/{(x – 3)(x + 3)}
    = {(3x^2 – x^2) – (7x – x) – (30 + 12)}/{(x – 3)(x + 3)}
    = {2x^2 – 6x – 42}/{(x – 3)(x + 3)}
    = {2x^2 – 6x – 42}/{x^2 – 9}
    b)
    {3x + 5}/{x^2 – 5x} + {25 – x}/{25 – 5x}                        (ĐKXĐ: x ne 5)
    = {3x + 5}/{x(x – 5)} + {25 – x}/{- (5x – 25)}
    = {3x + 5}/{x(x – 5)} – {25 – x}/{5x – 25}
    = {3x + 5}/{x(x – 5)} – {25 – x}/{5(x – 5)}
    = {5(3x + 5)}/{5x(x – 5)} – {x(25 – x)}/{5x(x – 5)}
    = {15x + 25}/{5x(x – 5)} – {25x – x^2}/{5x(x – 5)}
    = {15x + 25 – (25x – x^2)}/{5x(x – 5)}
    = {15x + 25 – 25x + x^2}/{5x(x – 5)}
    = {x^2 – 10x + 25}/{5x(x – 5)}
    = {x^2 – 2.x.5 + 5^2}/{5x(x – 5)}
    = {(x – 5)^2}/{5x(x – 5)}
    = {x – 5}/{5x}
    #SunHee

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222-9+11+12:2*14+14 = ? ( )

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