\(a,\dfrac{10x^3y^2}{20xy^5}=\dfrac{x^2}{2y^3}\\ b,\dfrac{15\left(x+5\right)^2}{20x\left(x+5\right)}=\dfrac{3\left(x+5\right)}{4x}\)

a) \(\dfrac{x^2}{2y^3}\)

b) \(\dfrac{3\left(x+5\right)}{4}\)=\(\dfrac{3x+15}{4}\)

a) \(\dfrac{10x^3y^2}{20xy^5}=\dfrac{x^2}{y^3}\)
b) \(\dfrac{15x\left(x+5\right)^2}{20x\left(x+5\right)}=\dfrac{x+5}{5x}\)

( x + 5 )³ - 15x( x + 10 )

= x³ + 15x² + 75x + 125 - 15x² - 150x

= x³ - 75x + 125

=15x²-(17x²-2x²-4x)

=15x²-15x²-4x

=4x

k cho mik nếu banh thấy đúng nhé!

\(\frac{15x\left(x+y\right)^3}{5y\left(x+y\right)^2}\)

ĐKXĐ : \(x+y\ne0\Leftrightarrow x\ne-y\)

\(=\frac{5\cdot3x\cdot\left(x+y\right)^2\left(x+y\right)}{5\cdot y\cdot\left(x+y\right)^2}\)

\(=\frac{3x\left(x+y\right)}{y}\)

`C4:`

`x/[x-2]+2/[2-x]=x/[x-2]-2/[x-2]=[x-2]/[x-2]=1`

`C5:[15x^2]/[17y^4] . [34y^5]/[15x^3]`

 `=[15x^2 . 2.17y^4 . y]/[17y^4 . 15x^2 . x]=[2y]/x`

`C5:[6x+18]/[(x+4)^2]:[3(x+3)]/[x+4]`

 `=[6(x+3)]/[(x+4)^2] . [x+4]/[3(x+3)]`

`=2/[x+4]`

a) \(\sqrt{\frac{3a}{4}}.\sqrt{\frac{4a}{27}}=\frac{\sqrt{3a}}{2}.\frac{\sqrt{4a}}{3\sqrt{3}}=\frac{\sqrt{3}.\sqrt{a}.2.\sqrt{a}}{6\sqrt{3}}=\frac{a.2\sqrt{3}}{6\sqrt{3}}=\frac{a}{3}\)

b) \(\sqrt{15x}.\sqrt{\frac{60}{x}}=\sqrt{15x}.\frac{2\sqrt{15}}{\sqrt{x}}=\frac{30\sqrt{x}}{\sqrt{x}}=30\)

a) \(\sqrt{\frac{3a}{4}}.\sqrt{\frac{4a}{27}}=\sqrt{\frac{3a}{4}.\frac{4a}{27}}=\sqrt{\frac{1}{9}.a^2}=\sqrt{\frac{1}{9}}.\sqrt{a^2}=\frac{1}{3}.a\)( Vì \(a\ge0\)nên \(\sqrt{a^2}=\left|a\right|=a\))

b) \(\sqrt{15x}.\sqrt{\frac{60}{x}}=\sqrt{15x.\frac{60}{x}}=\sqrt{900}=30\)

\(P=\dfrac{15x^5y^3-10x^3y^2+20x^4y^4}{5x^2y^2}\)

\(=\dfrac{15x^5y^3}{5x^2y^2}-\dfrac{10x^3y^2}{5x^2y^2}+\dfrac{20x^4y^4}{5x^2y^2}\)

\(=3x^3y-2x+4x^2y^2\)

Khi x=-1 và y=2 thì \(P=3\cdot\left(-1\right)^3\cdot2-2\cdot\left(-1\right)+4\cdot\left(-1\right)^2\cdot2^2\)

\(=-6+2+16=4+16=20\)

\(\left(1+\dfrac{100}{20}\right)\) x \(\dfrac{125}{60}\)

\(=6\) x \(\dfrac{125}{60}\)

\(=\dfrac{750}{60}=\dfrac{25}{2}\)