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a: Thay x=-3 vào A, ta được:
\(A=\dfrac{-3-5}{-3-4}=\dfrac{8}{7}\)
b: \(B=\dfrac{2}{x+5}+\dfrac{x+25}{\left(x+5\right)\left(x-5\right)}=\dfrac{2x-10+x+25}{\left(x+5\right)\left(x-5\right)}=\dfrac{3x+15}{\left(x-5\right)\left(x+5\right)}=\dfrac{3}{x-5}\)
c: Để M là số nguyên thì \(x-4\in\left\{1;-1;3;-3\right\}\)
hay \(x\in\left\{3;7;1\right\}\)
a) ĐKXĐ:
\(\left\{{}\begin{matrix}x^2-9\ne0\\x+3\ne0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x\ne\pm3\\x\ne-3\end{matrix}\right.\Leftrightarrow x\ne\pm3\)
b) \(A=\dfrac{x+15}{x^2-9}-\dfrac{2}{x+3}\)
\(A=\dfrac{x+15}{\left(x+3\right)\left(x-3\right)}-\dfrac{2\left(x-3\right)}{\left(x+3\right)\left(x-3\right)}\)
\(A=\dfrac{x+15-2x+6}{\left(x+3\right)\left(x-3\right)}\)
\(A=\dfrac{21-x}{\left(x+3\right)\left(x-3\right)}\)
c) Thay x = - 1 vào A ta có:
\(A=\dfrac{21-\left(-1\right)}{\left(-1+3\right)\left(-1-3\right)}=\dfrac{21+1}{2\cdot-4}=\dfrac{22}{-8}=-\dfrac{11}{4}\)
Câu 2:
a) \(A=\left(x+5\right)\left(2x-3\right)-2x\left(x+3\right)-\left(x-15\right)\)
\(=x\left(2x-3\right)+5\left(2x-3\right)-2x^2-6x-x+15\)
\(=2x^2-3x+10x-15-2x^2-6x-x+15\)
\(=0\)
b) \(B=2\left(x-5\right)\left(x+1\right)+\left(x+3\right)-\left(x-15\right)\)
\(=2\left[x\left(x+1\right)-5\left(x+1\right)\right]+x+3-x+15\)
\(=2.\left[\left(x^2+x\right)-\left(5x+5\right)\right]+x+3-x+15\)
\(=2.\left(x^2+x-5x-5\right)+x+3-x+15\)
\(=2x^2+2x-10x-10+x+3-x+15\)
\(=2x^2-8x+8\)
\(=2x\left(x-4\right)+8\)
Thay: \(x=\frac{3}{4}\) vào B ta đc:
\(2.\frac{3}{4}\left(\frac{3}{4}-4\right)+8\)
\(=\frac{3}{2}.\frac{-13}{4}+8\)
\(=\frac{25}{8}\)
c) \(C=5x^2\left(3x-2\right)-\left(4x+7\right)\left(6x^2-x\right)-\left(7x-9x^3\right)\)
\(=5x^23x-5x^22-\left[4x\left(6x^2-x\right)+7\left(6x^2-x\right)\right]-7x+9x^3\)
\(=15x^3-10x^2-\left[4x6x^2-4x^2+42x^2-7x\right]-7x+9x^3\)
\(=15x^3-10x^2-24x^3+4x^2-42x^2+7x-7x+9x^3\)
\(=-48x^2\)
P/s: Ko chắc!
`Answer:`
`a)`
`A=5(x+1)^2-3(x-3)^2-4(x^2-4)`
`=>A=5(x^2+2x+1)-3(x^2-6x+9)-4x^2+16`
`=>A=5x^2+10x+5-3x^2+18x-27-4x^2+16`
`=>A=(5x^2-3x^2-4x^2)+(10x+18x)+(5-27+16)`
`=>A=-2x^2+28x-6`
`b)`
`B=5(x+1)^2-3(x-3)^2-4(x+2)(x-2)`
`=2x(3x+5)-3(3x+5)-2x(x^2-4x+4)-[(2x)^2-3^2]`
`=6x^2+10x-9x-15-2x^3+8x^2-8x-4x^2+9`
`=(6x^2-4x^2+8x^2)-2x^3+(10x-9x-8x)+(-15+9)`
Thay `x=-7` vào ta được:
`B=10(-7)^2-2(-7)^3-7(-7)-6`
`=>B=10.49-2(-343)+49-6`
`=>B=490+686+49-6`
`=>B=1219`
Biến đổi ta được: m = 7 ( a + 1 ) ( 2 a − 5 ) ( 2 a + 5 ) ; n = 3 a ( 2 a + 5 ) 5 ( a 3 + 1 )
⇒ A = mn = 21 a ( 2 a − 5 ) ( a 2 − a + 1 )