Quy đồng mẫu các phân thức:
1) 7x-1/2x^2+6x; 3-2x/x^2-9
2) 2x-1/x-x^2; x+1/2-4x+2x^2
3) x-1/x^3+1; 2x/x^2-x+1; 2/x+1
4) 7/5x; 4/x-2y; x-y/8y^2-2x^2
5) x/x^3-1; x+1/x^2-x; x-1/x^2+x+1
6) x/x^2-2ax+a^2; x+a/x^2-ax
Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
\(a,\dfrac{7x-1}{2x^2+6x}=\dfrac{\left(7x-1\right)\left(x-3\right)}{2x\left(x+3\right)\left(x-3\right)}=\dfrac{7x^2-22x+3}{2x\left(x-3\right)\left(x+3\right)}\\ \dfrac{5-3x}{x^2-9}=\dfrac{2x\left(5-3x\right)}{2x\left(x-3\right)\left(x+3\right)}=\dfrac{10x-6x^2}{2x\left(x-3\right)\left(x+3\right)}\)
Ta có: 2 x 2 + 6 x = 2 x x + 3 ; x 2 - 9 = x + 3 x - 3
Mẫu thức chung: 2x(x + 3)(x – 3)
MT1: 2 x 2 + 6 x = 2 x ( x + 3 ) ; MT2: x 2 - 9 = ( x - 3 ) ( x + 3 )
MTC: 2x(x - 3)(x + 3)
NTP1: x – 3; NTP2: 2x
Quy đồng:
a ) MTC : \(2x\left(x+3\right)\left(x-3\right)\)
\(\frac{7x-1}{2x^2+6x}=\frac{7x-1}{2x\left(x+3\right)}=\frac{\left(7x-1\right)\left(x-3\right)}{2x\left(x+3\right)\left(x-3\right)}\)
\(\frac{3-2x}{x^2-9}=\frac{3-2x}{\left(x-3\right)\left(x+3\right)}=\frac{2x\left(3-2x\right)}{2x\left(x+3\right)\left(x-3\right)}\)
b ) MTC : \(2\left(-x\right)\left(x-1\right)^2\)
\(\frac{2x-1}{x-x^2}=\frac{2x-1}{-x\left(x-1\right)}=\frac{2\left(2x-1\right)\left(x-1\right)}{2\left(-x\right)\left(x-1\right)^2}\)
\(\frac{x+1}{2-4x+2x^2}=\frac{x+1}{2\left(x^2-2x+1\right)}=\frac{-x\left(x+1\right)}{2\left(-x\right)\left(x-1\right)^2}\)
Ta có:
Suy ra: x 3 - 7 x 2 + 7 x + 15 = x 2 - 4 x - 5 x - 3
Lại có:
Suy ra: x 3 - 7 x 2 + 7 x + 15 = x 2 - 2 x - 3 x - 5