Toán Lớp 8: Ta có B= $\frac{x+5}{2x}$-$\frac{x-6}{5-x}$-$\frac{2x^2-2x-50}{2x^2-10}$
chứng minh B= $\frac{x-5}{2x}$
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Toán Lớp 8: Ta có B= $\frac{x+5}{2x}$-$\frac{x-6}{5-x}$-$\frac{2x^2-2x-50}{2x^2-10}$
chứng minh B= $\frac{x-5}{2x}$
Comments ( 2 )
B = \frac{x + 5}{2x} – \frac{x – 6}{5 – x} – \frac{2x^{2}-2x-50 }{2x^{2}-10x)
B = \frac{x + 5}{2x} + \frac{x-6}{x-5}- \frac{2x^{2}-2x-50 }{2x. (x – 5)
B = \frac{(x+5). (x-5)+2x.(x-6)-(2x^{2}-2x-50)}{2x. (x – 5)}
B = \frac{x^{2}-25 + 2x^{2} -12x-2x^{2} +2x +50 }{2x. (x – 5)}
B = \frac{x^{2} – 10x +25}{2x. (x – 5)}
B = \frac{x^{2}-2.x.5 +5^{2}}{2x. (x – 5)
B = \frac{(x-5)^{2}}{2x. (x – 5)}
B = \frac{x-5}{2x} $\text{(đpcm)}$
Lời giải và giải thích chi tiết:
B=\frac{x+5}{2x}-\frac{x-6}{5-x}-\frac{2x^2-2x-50}{2x^2-10x}
=\frac{(x+5)(x-5)}{2x(x-5)}-\frac{2x(x-6)}{2x(5-x)}-\frac{2x^2-2x-50}{2x^2-10x}
=\frac{x^2-25}{2x^2-10x}-\frac{2x^2-12x}{10x-2x^2}-\frac{2x^2-2x-50}{2x^2-10x}
=\frac{x^2-25}{2x^2-10x}+\frac{2x^2-12x}{2x^2-10x}-\frac{2x^2-2x-50}{2x^2-10x}
=\frac{x^2-10x+25}{2x^2-10x}
=\frac{(x-5)^2}{2x(x-5)}
=\frac{x-5}{2x}
@Deawoo