Home
Class 9
MATHS
Prove that (a^(3/2)+ab)/(ab-b^3)-(sqrt(a...

Prove that `(a^(3/2)+ab)/(ab-b^3)-(sqrt(a))/(sqrt(a)-b)=(sqrt(a))/(b)`.

Text Solution

Verified by Experts

The correct Answer is:
`(sqrt(a))/(b)`
Promotional Banner

Topper's Solved these Questions

  • LAWS OF INDICES

    CALCUTTA BOOK HOUSE|Exercise EXERCISE - 6|67 Videos

  • HISTOGRAM AND FREQUENCY POLYGON

    CALCUTTA BOOK HOUSE|Exercise EXERCISE-2|16 Videos

  • LINEAR EQUATIONS

    CALCUTTA BOOK HOUSE|Exercise EXERCISE - 4.2|77 Videos

Similar Questions

Explore conceptually related problems

Three positive numbers a, b, c are in A.P. Prove that (1)/(sqrt(b)+sqrt(c )), (1)/(sqrt(c )+sqrt(a)) , (1)/(sqrt(a) + sqrt(b)) are also in A.P.

Prove that "tan"^(-1)sqrt((a(a+b+c))/(bc))+"tan"^(-1)sqrt((b(a+b+c))/(ca))+"tan"^(-1)sqrt((c(a+b+c))/(ab))=pi(a,b,c gt 0)

Ifint(dx)/(cos^3xsqrt(sin2x))=a(tan^2x+b)sqrt(tanx)+c ,t h e n (a) a=(sqrt(2))/5,b=1/(sqrt(5)) (b) a=(sqrt(2))/5,b=5 (c) a=(sqrt(2))/5,b=-1/(sqrt(5)) (d) a=(sqrt(2))/5, b=sqrt(5)

Prove that : (vii) log_(sqrt a)b.log_(sqrt(b))c.log_(sqrt(c ))a = 8 .

If a : b = c : d , then prove that (a +b)/(a - b) = sqrt(ac + ad + bc + bd)/sqrt(ac - ad - bc + bd) .

Values (s)(-i)^(1/3) is/are (sqrt(3)-i)/2 b. (sqrt(3)+i)/2 c. (-sqrt(3)-i)/2 d. (-sqrt(3)+i)/2

Prove that (a) sqrt(-sqrt3 + sqrt(3 + 8 sqrt(7 + 4 sqrt3))) =2 (b) sqrt(2- sqrt5 + sqrt(-15 + 4 sqrt(41 + 12 sqrt5))) =2

Find the term in (3sqrt(((a)/(sqrt(b))) + (sqrt((b)/ (3sqrt(a))))^(21) which has the same power of a and bdot

Which of the following is equal to root(3)(-1) a. (sqrt(3)+sqrt(-1))/2 b. (-sqrt(3)+sqrt(-1))/(sqrt(-4)) c. (sqrt(3)-sqrt(-1))/(sqrt(-4)) d. -sqrt(-1)

If a<0,b>0, then sqrt(a)sqrt(b) is equal to (a) -sqrt(|a|b) (b) sqrt(|a|b)i (c) sqrt(|a|b) (d) none of these

CALCUTTA BOOK HOUSE-LAWS OF INDICES-EXERCISE - 6
  1. Calculate : 9^(-3)xx((16)^(1/4))/(6^(-2))xx((1)/(27))^(-4/3).

    Text Solution

    |

  2. If x^y=y^x, then prove that (x/y)^(x/y)=(x)^((x)/(y)-1).

    Text Solution

    |

  3. Prove that (a^(3/2)+ab)/(ab-b^3)-(sqrt(a))/(sqrt(a)-b)=(sqrt(a))/(b).

    Text Solution

    |

  4. Show that (x^(b-c))^((1)/(bc))xx(x^(c-a))^((1)/(ca))xx(x^(a-b))^((1)/(...

    Text Solution

    |

  5. Factorise : (a+b).

    Text Solution

    |

  6. Find the value of ((bc)^(b-c)(ca)^(c-a)(ab)^(a-b))/((a^(b-c)b^(c-a)c^(...

    Text Solution

    |

  7. If p=a^x,q=a^y" and "a^2=(p^yq^x)^z, then find the value of xyz.

    Text Solution

    |

  8. If a^(m^n)= (a^m)^n, then express m in terms of n.

    Text Solution

    |

  9. If a^m a^n =a^(mn), then express m in terms of n.

    Text Solution

    |

  10. If x=2,y=4, then what is the value of x+2y+sqrt((x-2y)^2)?

    Text Solution

    |

  11. Which one is the greatest ? 3^(2^(2^2)), 3^(2.2.2), 3.2.2.2.

    Text Solution

    |

  12. Find the value of root(3)(x^4sqrt(x^(-5)sqrt(x^6))).

    Text Solution

    |

  13. Calculate : ((1)/(81))^(-5/4).

    Text Solution

    |

  14. Calculate : {root(3)(4)xx(1)/(root(6)(8))xxroot(12)(2^(-1))}^(3/4).

    Text Solution

    |

  15. Simplify : x^(1/3).x^(-1/4).x^(-1/2) divx^(-(7)/(12))

    Text Solution

    |

  16. Simplify : root(4)(a^2b^3c^4)xxroot(3)(a^4b^6)xx(a^(1/2)b^(1/3)c^(1/4)...

    Text Solution

    |

  17. Simplify : {(a)^(n^(2)-1)}^((n)/(n+1))xx(sqrt(a^(2n)))/(a).

    Text Solution

    |

  18. Simplify : ((p+(1)/(q))^m(p-(1)/(q))^n)/((q+(1)/(p))^m(q-(1)/(p))^n).

    Text Solution

    |

  19. Simplify : (2^n.6^(m+1).10^(m-n).15^(m+n-2))/(4^m.3^(m+n).25^(m-1)).

    Text Solution

    |

  20. Simplify : (x^((b+c)/(c-a)))^((1)/(a-b))xx(x^((c+a)/(a-b)))^((1)/(b-c)...

    Text Solution

    |