Why Does Adding 's' Change to Subtracting 'c' in This Algebraic Expression?

[roadworx]

Hi,

I have:

$$\frac{a}{b+a+s} + \frac{c*b}{(b+a+s)(c+s)}$$

I can rearrange that to:

$$\frac{a-c}{b+a-c} * \frac{b+a}{b+a+s} + \frac{b}{b+a-c} * \frac{c}{c+s}$$

Is this correct? If so, can someone tell me why the +s changes into a -c?

 

[mathman]

You should supply the steps. Also what are you trying to achieve?
A simpler expression is (ac + as + bc)/[(b + a + s)(c + s)].

 

[Mark44]

Hi,

I have:

$$\frac{a}{b+a+s} + \frac{c*b}{(b+a+s)(c+s)}$$

I can rearrange that to:

$$\frac{a-c}{b+a-c} * \frac{b+a}{b+a+s} + \frac{b}{b+a-c} * \frac{c}{c+s}$$

Is this correct? If so, can someone tell me why the +s changes into a -c?

If your goal is to combine the two rational expressions, multiply the one on the left by 1 in the form of (c + s)/(c + s). That gives you the same denominator in both expressions, so you can then add the numerators.

A +s should not change to a -c.