1. ## simplify expressions

WOULD SOMEONE HELP ME WITH THESE SUMS ? HERE ARE THEY :
1. SOLVE FOR x :

1/(X) - 1/(X+6 )= 1/(A) - 1/(A+B)

2. SIMPLIFY:

A/(A-X) + B/(B-X) + C/( C-X)
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3/(X) - 1/(X-A) - 1/(X-B) - 1/(X-C)

3. SIMPLIFY :

A2/(X-A) + B2/(X-B) + C2/(X-C) + A + B + C
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A/(X-A) + B/(X-B) + C/(X-C)

2. Could you use (parentheses) to clarify what the denominators are?

3. Hello,

Originally Posted by sabyasachi
WOULD SOMEONE HELP ME WITH THESE SUMS ? HERE ARE THEY :
1. SOLVE FOR x :

1/(X) - 1/(X+6 )= 1/(A) - 1/(A+B)
$\frac 1X-\frac{1}{X+6}=\frac 1A-\frac{1}{A+B}$

$\frac 1X-\frac{1}{X+6}=\frac{X+6}{X(X+6)}-\frac{X}{X(X+6)}=\boxed{\frac{6}{X(X+6)}}$
And :
$\frac 1A-\frac{1}{A+B}=\frac{A+B}{A(A+B)}-\frac{A}{A(A+B)}=\boxed{\frac{B}{A(A+B)}}$

The equation is now :

$\frac{6}{X(X+6)}=\frac{B}{A(A+B)}$

Taking the inverse :

$\frac 16 \cdot X(X+6)=\frac 1B \cdot A(A+B)$

$X(X+6)=\frac 6B \cdot A(A+B)$

Can you continue ?

please can you help me further with that sum?

5. Originally Posted by sabyasachi
please can you help me further with that sum?
Develop and solve... But I don't know your level and whether you know about discriminants or not ~

6. ## got it

well i m sorry.i just can't sit idle without solving those sums. moo did try to help me but he/she left a certain portion of a sum to be solved by me.but i was still confused a it.

7. ## Well I Don't

Well! I Do Not Know About Discriminants Yet. Please Solve The Sum Step-by-step And In Simple Language/method. Much Obliged.

8. Actually, without any further information about A and B, the equation can have no solution... So please post everything you have ~

There is a direct solution : X=A and B=6.

9. ## I Know

Well I Do Know A Bit About Solving Linear, Quadratic Equations Etc. Now I Realize That I Do Know About Discriminants, But I Did Not Know The Exact Term Prior To This.

10. Ok.

Then, we have :

Originally Posted by Moo

$X(X+6)=\frac 6B \cdot A(A+B)$
$X^2+6X=\underbrace{\frac 6B \cdot A(A+B)}_{M}$

$X^2+6X-M=0$

$\Delta=36+4M$

--> $\sqrt{\Delta}=\sqrt{36+4M}=\sqrt{4(9+M)}=2\sqrt{9+ M}$

$X=\frac{-6 \pm 2\sqrt{9+M}}{2}=-3 \pm \sqrt{9+M}$

And $9+M$ has to be $\ge 0$, that is to say $M \ge -9 \Longleftrightarrow \frac 6B \cdot A(A+B) \ge -9 \Longleftrightarrow 2A(A+B) \ge -3B$

And I don't think we can go further.

This Problem Is Meant For Students Of Class 8 ( In India). Please Simplify Your Method. I Could Understand Till The Inversion,but Faltered While Solving The Remaining Portion.

12. Originally Posted by sabyasachi
This Problem Is Meant For Students Of Class 8 ( In India). Please Simplify Your Method. I Could Understand Till The Inversion,but Faltered While Solving The Remaining Portion.
$\Delta$ is the discriminant..

When you have an equation : $ax^2+bx+c=0$, $\Delta=b^2-4ac$

Thus the solutions are $x=\frac{-b \pm \sqrt{\Delta}}{2a}$

If you have never dealt with discriminants, you can't solve generally this equation.

A particular solution to this is : $X=A$ and $B=6$, because the two sides of the equation are similar.

13. ## At Last

Thanks A Lot. If We Can Arrive At The Solution According To Mathematical Methods, Please Solve It.

14. Originally Posted by sabyasachi
Thanks A Lot. If We Can Arrive At The Solution According To Mathematical Methods, Please Solve It.
This is a mathematical method...

There are so many unknown things that we can't provide a decent solution apart from the one I wrote just above..

15. ## Something More

Thank You For Helping Me.i Troubled You The Whole Day.but Now Can You Help Me With The Other Sums (2 Of Them)? I Know You Are Getting Irritated.

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