Toán Lớp 8: Thực hiện phép tính
a) $\frac{10}{x^2-25}$ -$\frac{5}{x^2+5x}$
b) $\frac{4x}{2x+1}+$ $\frac{2}{2x+1}$
c) $\frac{3x^2+3x+3}{4x+4}$ :$\frac{9x^3-9}{2x^2-2}$
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Toán Lớp 8: Thực hiện phép tính
a) $\frac{10}{x^2-25}$ -$\frac{5}{x^2+5x}$
b) $\frac{4x}{2x+1}+$ $\frac{2}{2x+1}$
c) $\frac{3x^2+3x+3}{4x+4}$ :$\frac{9x^3-9}{2x^2-2}$
Comments ( 2 )
Giải đáp+Lời giải và giải thích chi tiết:
a)
10/{x^2 – 25} – 5/{x^2 + 5x} (ĐKXĐ: x ne 0 ; x ne +- 5)
= 10/{x^2 – 5^2} – 5/{x(x + 5)}
= 10/{(x – 5)(x + 5)} – 5/{x(x + 5)}
= {10x}/{x(x – 5)(x + 5)} – {5(x – 5)}/{x(x + 5)(x – 5)}
= {10x}/{x(x – 5)(x + 5)} – {5x – 25}/{x(x + 5)(x – 5)}
= {10x – (5x – 25)}/{x(x + 5)(x – 5)}
= {10x – 5x + 25}/{x(x + 5)(x – 5)}
= {5x + 25}/{x(x + 5)(x – 5)}
= {5(x + 5)}/{x(x + 5)(x – 5)}
= 5/{x(x – 5)}
= 5/{x^2 – 5x}
b)
{4x}/{2x + 1} + 2/{2x + 1} (ĐKXĐ: x ne – 1/2)
= {4x + 2}/{2x + 1}
= {2(2x + 1)}/{2x + 1}
= 2
c)
{3x^2 + 3x + 3}/{4x + 4} : {9x^3 – 9}/{2x^2 – 2}
= {3(x^2 + x + 1)}/{4(x + 1)} : {9(x^3 – 1)}/{2(x^2 – 1)}
= {3(x^2 + x + 1)}/{4(x + 1)} . {2(x^2 – 1)}/{9(x^3 – 1)}
= {3(x^2 + x + 1)}/{4(x + 1)} . {2(x – 1)(x + 1)}/{9(x – 1)(x^2 + x + 1)}
= {3}/{4} . {2(x – 1)}/{9(x – 1)}
= 3/4 . 2/9
= 1/2 . 1/3
= 1/6
#SunHee
Giải đáp:
Lời giải và giải thích chi tiết:
a;[10]/[x^2 -25]-5/[x^2 +5x](đk:x\ne0;-5;5)
=[10]/[(x-5)(x+5)]-5/[x(x+5)]
=[10x-5(x-5)]/[x(x-5)(x+5)]
=[10x-5x+25]/[x(x-5)(x+5)]
=[5x+25]/[x(x-5)(x+5)]
=[5(x+5)]/[x(x-5)(x+5)]
=5/[x(x-5)]
b;[4x]/[2x+1]+2/[2x+1](đk:x\ne-1/2)
=[4x+2]/[2x+1]
=[2(2x+1)]/[2x+1]
=2
c;[3x^2 +3x+3]/[4x+4]:[9x^3 -9]/[2x^2 -2](đk:x\ne-1;1)
=[3(x^2 +x+1)]/[4(x+1)].[2(x-1)(x+1)]/[9(x-1)(x^2 +x+1)]
=[3(x^2 +x+1)]/[4(x+1)].[2(x+1)]/[9(x^2 +x+1)]
=3/4 . 2/9
=1/[2.3]
=1/6