SOLUTION: We are doing Jacob's Algebra at home. We are on Lesson 3 in Chapter 15 Set III Question 9 c Here is what we have tried for days! 2x/x+5 - 3/x-2 = 1 First we multiplied both si

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Question 5835: We are doing Jacob's Algebra at home.
We are on Lesson 3 in Chapter 15
Set III Question 9 c
Here is what we have tried for days!
2x/x+5 - 3/x-2 = 1
First we multiplied both sides by (x+5)(x-2) to get
2x^2-4x-3x+15=(x+5) (x-2)
2x^2-7x+15 = x^2=5x-2x-10
x^2-10x+25=0
When we did the quadratic formula to get the answer we got the answer of just 5
but the answer in the book is
10.48 and -.48
So then we tried
multiplying each side by (x^2 +10)
(we weren't sure if we should maybe do (x^2 - 10), which could also work)
and we got these answers 4.52 and -5.52
which are also wrong!
Please let us know what to multiply by to get the right answer!
Thanks!
We will be checking all the time for your response! Thanks so much!
Julie Cochran
julie-cochran@earthlink.net
Answer by ichudov(507) About Me  (Show Source):
You can put this solution on YOUR website!
great job trying!
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • This is an equation! Solutions: x=10.4772255750517,x=-0.477225575051661.
  • Graphical form: Equation 2x%2A%28x-2%29-3%2A%28x%2B5%29=%28x-2%29%2A%28x%2B5%29 was fully solved.
  • Text form: 2x*(x-2)-3*(x+5)=(x-2)*(x+5) simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+2x%2A%28x-2%29-3%2A%28x%2B5%29=%28x-2%29%2A%28x%2B5%29+%29
    For tutors: simplify_cartoon( 2x*(x-2)-3*(x+5)=(x-2)*(x+5) )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at 2%2Ax%2A%28x-2%29-3%2A%28x%2B5%29=highlight_red%28+%28x-2%29%2A%28x%2B5%29+%29.
Moved these terms to the left highlight_green%28+-%28x-2%29%2A%28x%2B5%29+%29
It becomes 2%2Ax%2A%28x-2%29-3%2A%28x%2B5%29-highlight_green%28+%28x-2%29%2A%28x%2B5%29+%29=0.
Look at highlight_red%28+2%2Ax%2A%28x-2%29+%29-3%2A%28x%2B5%29-%28x-2%29%2A%28x%2B5%29=0.
Expanded term 2%2Ax by using associative property on %28x-2%29
It becomes .
Look at .
Multiplied numerator integers
It becomes 2%2Ax%2Ax-highlight_green%28+4+%29%2Ax-3%2A%28x%2B5%29-%28x-2%29%2A%28x%2B5%29=0.
Look at .
Reduce similar several occurrences of highlight_red%28+x+%29 to highlight_green%28+x%5E2+%29
It becomes 2%2Ahighlight_green%28+x%5E2+%29-4%2Ax-3%2A%28x%2B5%29-%28x-2%29%2A%28x%2B5%29=0.
Look at 2%2Ax%5E2-4%2Ax-highlight_red%28+3%2A%28x%2B5%29+%29-%28x-2%29%2A%28x%2B5%29=0.
Expanded term -3 by using associative property on %28x%2B5%29
It becomes .
Look at .
Multiplied numerator integers
It becomes 2%2Ax%5E2-4%2Ax-3%2Ax-highlight_green%28+15+%29-%28x-2%29%2A%28x%2B5%29=0.
Look at 2%2Ax%5E2-4%2Ax-3%2Ax-highlight_red%28+15+%29-%28x-2%29%2A%28x%2B5%29=0.
Moved -15 to the right of expression
It becomes 2%2Ax%5E2-4%2Ax-3%2Ax-%28x-2%29%2A%28x%2B5%29-highlight_green%28+15+%29=0.
Look at 2%2Ax%5E2-highlight_red%28+4%2Ax+%29-highlight_red%28+3%2Ax+%29-%28x-2%29%2A%28x%2B5%29-15=0.
Eliminated similar terms highlight_red%28+-4%2Ax+%29,highlight_red%28+-3%2Ax+%29 replacing them with highlight_green%28+%28-4-3%29%2Ax+%29
It becomes 2%2Ax%5E2%2Bhighlight_green%28+%28-4-3%29%2Ax+%29-%28x-2%29%2A%28x%2B5%29-15=0.
Look at .
Added fractions or integers together
It becomes 2%2Ax%5E2%2B%28highlight_green%28+-7+%29%29%2Ax-%28x-2%29%2A%28x%2B5%29-15=0.
Look at 2%2Ax%5E2%2B%28highlight_red%28+-7+%29%29%2Ax-%28x-2%29%2A%28x%2B5%29-15=0.
Removed extra sign in front of -7
It becomes 2%2Ax%5E2%2B%28-highlight_green%28+7+%29%29%2Ax-%28x-2%29%2A%28x%2B5%29-15=0.
Look at .
Remove unneeded parentheses around factor highlight_red%28+7+%29
It becomes 2%2Ax%5E2-highlight_green%28+7+%29%2Ax-%28x-2%29%2A%28x%2B5%29-15=0.
Look at 2%2Ax%5E2-7%2Ax-highlight_red%28+%28x-2%29%2A%28x%2B5%29+%29-15=0.
Expanded term -%28x%2B5%29 by using associative property on %28x-2%29
It becomes .
Look at 2%2Ax%5E2-7%2Ax-highlight_red%28+%28x%2B5%29%2Ax+%29%2B%28x%2B5%29%2A2-15=0.
Expanded term -x by using associative property on %28x%2B5%29
It becomes .
Look at 2%2Ax%5E2-7%2Ax-highlight_red%28+x+%29%2Ahighlight_red%28+x+%29-x%2A5%2B%28x%2B5%29%2A2-15=0.
Reduce similar several occurrences of highlight_red%28+x+%29 to highlight_green%28+x%5E2+%29
It becomes 2%2Ax%5E2-7%2Ax-highlight_green%28+x%5E2+%29-x%2A5%2B%28x%2B5%29%2A2-15=0.
Look at highlight_red%28+2%2Ax%5E2+%29-7%2Ax-highlight_red%28+x%5E2+%29-x%2A5%2B%28x%2B5%29%2A2-15=0.
Eliminated similar terms highlight_red%28+2%2Ax%5E2+%29,highlight_red%28+-x%5E2+%29 replacing them with highlight_green%28+%282-1%29%2Ax%5E2+%29
It becomes highlight_green%28+%282-1%29%2Ax%5E2+%29-7%2Ax-x%2A5%2B%28x%2B5%29%2A2-15=0.
Look at .
Eliminated similar terms highlight_red%28+-7%2Ax+%29,highlight_red%28+-x%2A5+%29 replacing them with highlight_green%28+%28-7-5%29%2Ax+%29
It becomes %282-1%29%2Ax%5E2%2Bhighlight_green%28+%28-7-5%29%2Ax+%29%2B%28x%2B5%29%2A2-15=0.
Look at highlight_red%28+%282-1%29+%29%2Ax%5E2%2B%28-7-5%29%2Ax%2B%28x%2B5%29%2A2-15=0.
Remove extraneous '1' from product highlight_red%28+%282-1%29+%29
It becomes x%5E2%2B%28-7-5%29%2Ax%2B%28x%2B5%29%2A2-15=0.
Look at x%5E2%2B%28-highlight_red%28+7+%29-highlight_red%28+5+%29%29%2Ax%2B%28x%2B5%29%2A2-15=0.
Added fractions or integers together
It becomes x%5E2%2B%28highlight_green%28+-12+%29%29%2Ax%2B%28x%2B5%29%2A2-15=0.
Look at x%5E2%2B%28highlight_red%28+-12+%29%29%2Ax%2B%28x%2B5%29%2A2-15=0.
Removed extra sign in front of -12
It becomes x%5E2%2B%28-highlight_green%28+12+%29%29%2Ax%2B%28x%2B5%29%2A2-15=0.
Look at x%5E2%2Bhighlight_red%28+%28-highlight_red%28+12+%29%29%2Ax+%29%2B%28x%2B5%29%2A2-15=0.
Remove unneeded parentheses around factor highlight_red%28+12+%29
It becomes x%5E2-highlight_green%28+12+%29%2Ax%2B%28x%2B5%29%2A2-15=0.
Look at x%5E2-12%2Ax%2Bhighlight_red%28+%28x%2B5%29%2A2+%29-15=0.
Expanded term 2 by using associative property on %28x%2B5%29
It becomes x%5E2-12%2Ax%2Bhighlight_green%28+2%2Ax+%29%2Bhighlight_green%28+2%2A5+%29-15=0.
Look at x%5E2-12%2Ax%2B2%2Ax%2Bhighlight_red%28+2+%29%2Ahighlight_red%28+5+%29-15=0.
Multiplied numerator integers
It becomes x%5E2-12%2Ax%2B2%2Ax%2Bhighlight_green%28+10+%29-15=0.
Look at x%5E2-12%2Ax%2B2%2Ax%2Bhighlight_red%28+10+%29-highlight_red%28+15+%29=0.
Added fractions or integers together
It becomes x%5E2-12%2Ax%2B2%2Ax%2Bhighlight_green%28+-5+%29=0.
Look at x%5E2-12%2Ax%2B2%2Ax%2Bhighlight_red%28+-5+%29=0.
Removed extra sign in front of -5
It becomes x%5E2-12%2Ax%2B2%2Ax-highlight_green%28+5+%29=0.
Look at x%5E2-highlight_red%28+12%2Ax+%29%2Bhighlight_red%28+2%2Ax+%29-5=0.
Eliminated similar terms highlight_red%28+-12%2Ax+%29,highlight_red%28+2%2Ax+%29 replacing them with highlight_green%28+%28-12%2B2%29%2Ax+%29
It becomes x%5E2%2Bhighlight_green%28+%28-12%2B2%29%2Ax+%29-5=0.
Look at x%5E2%2B%28-highlight_red%28+12+%29%2Bhighlight_red%28+2+%29%29%2Ax-5=0.
Added fractions or integers together
It becomes x%5E2%2B%28highlight_green%28+-10+%29%29%2Ax-5=0.
Look at x%5E2%2B%28highlight_red%28+-10+%29%29%2Ax-5=0.
Removed extra sign in front of -10
It becomes x%5E2%2B%28-highlight_green%28+10+%29%29%2Ax-5=0.
Look at x%5E2%2Bhighlight_red%28+%28-highlight_red%28+10+%29%29%2Ax+%29-5=0.
Remove unneeded parentheses around factor highlight_red%28+10+%29
It becomes x%5E2-highlight_green%28+10+%29%2Ax-5=0.
Look at highlight_red%28+x%5E2-10%2Ax-5+%29=0.
Equation highlight_red%28+x%5E2-10%2Ax-5=0+%29 is a quadratic equation: x^2-10*x-5 =0, and has solutions 10.4772255750517,-0.477225575051661
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: x=10.4772255750517,x=-0.477225575051661.

Universal Simplifier and Solver


Done!