Solve [math]x-1=\frac{x^2-4x+3}{x+2}[/math] for [math]x[/math].

Solve[math]\frac{4}{4-x}=\frac{5}{4+x}[/math] for [math]x[/math].

Using the app, show that the equation [math]\frac{1}{60}=\frac{2x+50}{x(x+50)}[/math] is equivalent to [math]x^2-70x-3,000=0[/math] for all values of [math]x[/math] not equal to 0 or -50. Explain each step as you rewrite the original equation.

Kiran jogs at a speed of 6 miles per hour when there are no hills. He plans to jog up a mountain road, which will cause his speed to decrease by [math]r[/math] miles per hour. Which expression represents the time, [math]t[/math], in hours it will take him to jog 8 miles up the mountain road?

The rational function [math]g(x)=\frac{x+10}{x}[/math] can be rewritten in the form [math]g(x)=c+\frac{r}{x}[/math], where [math]c[/math] and [math]r[/math] are constants. Which expression is the result?

[size=150]For each equation below, find the value(s) of [math]x[/math] that make it true.[/size][br][br][math]10=\frac{1+7x}{7+x}[/math]

[math]0.2=\frac{6+2x}{12+x}[/math]

[math]0.8=\frac{x}{0.5+x}[/math]

[math]3.5=\frac{4+2x}{0.5-x}[/math]

A softball player has had 8 base hits out of 25 at bats for a current batting average of [math]\frac{8}{25}=.320[/math].[br][br]How many consecutive base hits does she need if she wants to raise her batting average to .400? Explain or show your reasoning.