# ACT Math 2.1 Intermediate Algebra

ACT Math Intermediate Algebra Drill 2, Problem 1. Solve the equation.

ACT Math | Intermediate Algebra |

ACT Mathematics | Intermediate Algebra |

Algebra | Factoring Interpret the structure of expressions Write expressions in equivalent forms to solve problems |

Elementary Algebra | Solve quadratic equations by factoring |

Foreign Language | Arabic Subtitled Chinese Subtitled Korean Subtitled Spanish Subtitled |

Intermediate Algebra | Fractional equations Radical and rational expressions |

Language | English Language |

Product Type | ACT Math |

### Transcript

One: multiplying by the inverse -- so we have to flip the 2nd fraction around and make

it times rather than divided by...

And then two: We clearly have a factorable expression here.

For the first one we have an a in each of these parts of the parentheses...

...then we have to figure out what 2 numbers multiply together to get negative 12 and also

add together to get negative 1.

What are the factors of 12? 1 and 12? Yeah... but that won't work.

2 and 6 don't work either, because when added, no matter which is positive and which

is negative, they won't total "1."

3 and 4 however... DO work.

So we want the ADDED part to be a negative 1... negative 4 plus 3 is negative 1, and

negative 4 times 3 is negative 12, so... we're good.

The first part of our answer is quantity a plus 3 times quantity a minus 4.

Now to the denominator.

We need 2 numbers that when multiplied are 2... and when added are 3.

Well... 2 only has 2 and 1 as factors... and luckily, if we add 2 and 1 we get 3. So the

bottom is a quick calculation.

It's quantity a plus 2 times quantity a plus 1.

Now we just rewrite everything so it's fully factored and... cross-out-able.

The quantity a plus 3 over the quantity a plus 3 becomes 1; we can trash it.

Same deal with the quantity a plus 2.

And we are left with just quantity a minus 4 over a plus 1...

...and the answer is C.

Phew.