How do you solve #7/(x-4) = 1 + 9/(x+4)#?
2 Answers
Explanation:
first, a common denominator for all the fractions needs to be found.
this is the lowest common multiple of
since
this gives
the denominator can then be taken away by multiplying everything by
then the brackets can be expanded:
(difference of two squares identity:
collect like terms:
then subtract
subtract
this forms a quadratic eqaution that can be factorised.
to do this, find two numbers that add to make
and multiply to make
for the number on the right-hand side to be
either
if
if
this means that the two possible values for
Explanation:
1) Give the addends on the right side a common denominator
2) Add the like fractions on the right by adding the numerators and keeping the common denominator
3) Combine like terms in the numerator on the right
4) Clear the first fraction by multiplying both sides by
5) Clear the second fraction by multiplying both sides by
6) Clear the parentheses by distributing the
7) Subtract
8) Set the equation to
9) Factor
10) Set the factors equal to
Answer:
Check
Sub in
Reduce the fraction to lowest terms