​x+31​−x−32​=(x−3)⋅(x+3)3⋅(x+5)​+x+31​−x−32​
x2−93x+15​+x+31​−x−32​=(x−3)⋅(x+3)3⋅(x+5)​+x+31​−x−32​=(x−3)⋅(x+3)3⋅(x+5)​+(x+3)⋅(x−3)x−3​−(x−3)⋅(x+3)2⋅(x+3)​\(=\frac{3\cdot\left(\right.x+5\left.\right)+x-3-2\cdot\left(\right.x+3\left.\right)}{\left(\right.x-3\left.\right)\cdot\left(\right.x+3\left.\right)}=\frac{3x+15+x-3-2x-6}{\left(\right.x-3\left.\right)\cdot\left(\right.x+3\left.\right)}=\frac{2x+6}{\left(\right.x+3\left.\right)\cdot\left(\right.x-3\left.\right)}=\frac{2\cdot\left(\right.x+3\left.\right)}{\left(\right.x+3\left.\right)\cdot\left(\right.x-3\left.\right)}=\frac{2}{x-3}\)

câu b

để \(\frac{2}{x-3}=\frac{2}{3}\) thì \(x-3=3\)

\(\Rightarrow x=3+3=6\)

vậy  \(x=6\) thì \(x=\frac{2}{3}\)

​x+31​−x−32​=(x−3)⋅(x+3)3⋅(x+5)​+x+31​−x−32​
x2−93x+15​+x+31​−x−32​=(x−3)⋅(x+3)3⋅(x+5)​+x+31​−x−32​=(x−3)⋅(x+3)3⋅(x+5)​+(x+3)⋅(x−3)x−3​−(x−3)⋅(x+3)2⋅(x+3)​\(=\frac{3\cdot\left(\right.x+5\left.\right)+x-3-2\cdot\left(\right.x+3\left.\right)}{\left(\right.x-3\left.\right)\cdot\left(\right.x+3\left.\right)}=\frac{3x+15+x-3-2x-6}{\left(\right.x-3\left.\right)\cdot\left(\right.x+3\left.\right)}=\frac{2x+6}{\left(\right.x+3\left.\right)\cdot\left(\right.x-3\left.\right)}=\frac{2\cdot\left(\right.x+3\left.\right)}{\left(\right.x+3\left.\right)\cdot\left(\right.x-3\left.\right)}=\frac{2}{x-3}\)

câu b

để \(\frac{2}{x-3}=\frac{2}{3}\) thì \(x-3=3\)

\(\Rightarrow x=3+3=6\)

vậy  \(x=6\) thì \(x=\frac{2}{3}\)

a, ta có đường cao:AH

=>AH vuông góc BC =>AHB=90`

Tam giác ABC vuông tại A

=>ABC=90`

Xét hai tam giác ABC và AHB có

AHB=ABC={90`}

chung góc B

=>tam giác ABC~AHB(g-c-g)

=>\(\frac{AB}{HB}\) \(=\frac{BC}{BA}\) (các cạnh tương ứng)

=> AB.BA=HB.BC \(AB^2\) =BC.BH

b,

Goi quang duong AB{km,x>0}

van toc trung binh la 15km/h nen van toc trung binh luc ve la:\(2\times15-12=18\)

Thoi gian di la:\(\frac{x}{12}\)

thoi gian ve la:\(\frac{x}{18}\)

Luc ve nhieu hon luc di ta co phuong trinh:

\(\frac{x}{12}-\frac{x}{18}\) \(=\frac34\)

<=>x{\(\frac{1}{12}-\frac{1}{18}\) }\(=\frac34\)

\(x\times\frac{1}{36}=\frac34\)

x=\(\frac34:\frac{1}{36}\)

x=27 km

vay nghiem cua phuong trinh la x=27km

Goi quang duong AB{km,x>0}

van toc trung binh la 15km/h nen van toc trung binh luc ve la:\(2\times15-12=18\)

Thoi gian di la:\(\frac{x}{12}\)

thoi gian ve la:\(\frac{x}{18}\)

Luc ve nhieu hon luc di ta co phuong trinh:

\(\frac{x}{12}-\frac{x}{18}\) \(=\frac34\)

<=>x{\(\frac{1}{12}-\frac{1}{18}\) }\(=\frac34\)

\(x\times\frac{1}{36}=\frac34\)

x=\(\frac34:\frac{1}{36}\)

x=27 km

vay nghiem cua phuong trinh la x=27km

Goi quang duong AB{km,x>0}

van toc trung binh la 15km/h nen van toc trung binh luc ve la:\(2\times15-12=18\)

Thoi gian di la:\(\frac{x}{12}\)

thoi gian ve la:\(\frac{x}{18}\)

Luc ve nhieu hon luc di ta co phuong trinh:

\(\frac{x}{12}-\frac{x}{18}\) \(=\frac34\)

<=>x{\(\frac{1}{12}-\frac{1}{18}\) }\(=\frac34\)

\(x\times\frac{1}{36}=\frac34\)

x=\(\frac34:\frac{1}{36}\)

x=27 km

vay nghiem cua phuong trinh la x=27km

Goi quang duong AB{km,x>0}

van toc trung binh la 15km/h nen van toc trung binh luc ve la:\(2\times15-12=18\)

Thoi gian di la:\(\frac{x}{12}\)

thoi gian ve la:\(\frac{x}{18}\)

Luc ve nhieu hon luc di ta co phuong trinh:

\(\frac{x}{12}-\frac{x}{18}\) \(=\frac34\)

<=>x{\(\frac{1}{12}-\frac{1}{18}\) }\(=\frac34\)

\(x\times\frac{1}{36}=\frac34\)

x=\(\frac34:\frac{1}{36}\)

x=27 km

vay nghiem cua phuong trinh la x=27km

Goi quang duong AB{km,x>0}

van toc trung binh la 15km/h nen van toc trung binh luc ve la:\(2\times15-12=18\)

Thoi gian di la:\(\frac{x}{12}\)

thoi gian ve la:\(\frac{x}{18}\)

Luc ve nhieu hon luc di ta co phuong trinh:

\(\frac{x}{12}-\frac{x}{18}\) \(=\frac34\)

<=>x{\(\frac{1}{12}-\frac{1}{18}\) }\(=\frac34\)

\(x\times\frac{1}{36}=\frac34\)

x=\(\frac34:\frac{1}{36}\)

x=27 km

vay nghiem cua phuong trinh la x=27km

Goi quang duong AB{km,x>0}

van toc trung binh la 15km/h nen van toc trung binh luc ve la:\(2\times15-12=18\)

Thoi gian di la:\(\frac{x}{12}\)

thoi gian ve la:\(\frac{x}{18}\)

Luc ve nhieu hon luc di ta co phuong trinh:

\(\frac{x}{12}-\frac{x}{18}\) \(=\frac34\)

<=>x{\(\frac{1}{12}-\frac{1}{18}\) }\(=\frac34\)

\(x\times\frac{1}{36}=\frac34\)

x=\(\frac34:\frac{1}{36}\)

x=27 km

vay nghiem cua phuong trinh la x=27km

Goi quang duong AB{km,x>0}

van toc trung binh la 15km/h nen van toc trung binh luc ve la:\(2\times15-12=18\)

Thoi gian di la:\(\frac{x}{12}\)

thoi gian ve la:\(\frac{x}{18}\)

Luc ve nhieu hon luc di ta co phuong trinh:

\(\frac{x}{12}-\frac{x}{18}\) \(=\frac34\)

<=>x{\(\frac{1}{12}-\frac{1}{18}\) }\(=\frac34\)

\(x\times\frac{1}{36}=\frac34\)

x=\(\frac34:\frac{1}{36}\)

x=27 km

vay nghiem cua phuong trinh la x=27km