Rational Expressions and Functions 1

The rational expression below simplifies to

$$\frac{a}{x-1}$$

What replaces a in the simplified form?

$$\frac{x\left(x+3\right)}{x^2+2x-3}$$

(a)  

The rational expression below simplifies to

$$\frac{x-a}{x-4}$$

What replaces a in this simplified form?

$$\frac{x^2-3x+2}{x^2-5x+4}$$

(a)  

The rational expression below simplifies to

$$\frac{a}{y-3}$$

What replaces the a in the simplified expression?

$$\frac{y^2+10y+21}{\left(y+7\right)\left(y^2-9\right)}$$

(a)  

If

$$\frac{x^5y^3}{zy^7}\div\frac{x^3z^2}{z^5y^2}=\frac{x^az^2}{y^2}$$ ,

what replaces a in the answer?

(a)  

If

$$\frac{x+y}{6}\div\frac{x^2-y^2}{3}=\frac{1}{a\left(x-y\right)}$$ ,

what is the value of a in the answer?

(a)