How do you simplify this equation?: b+10/ 4b-20 - 4b+20/ 5b-25

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violy's profile pic

violy | High School Teacher | (Level 1) Associate Educator

Posted on

We first factor the denominators separately.

`4b - 20 = 4(b - 5)` and `5b - 25 = 5(b - 5)`

Therefore, teh lcd = 4 * 5 (b - 5) = 20(b - 5).

We will make the denominators equal to the lcd. 

`((b + 10) * (5))/((4(b - 5))*(5)) - ((4b + 20)*(4))/((5(b - 5))*(4))`

Use Distributive property on top. 

`(5b + 50 - (16b + 80))/(20(b - 5))`

Change the signs of the subtrahend, and proceed on the rules of Addition.

`(5b + 50 + (-16b) + (-80))/(20(b - 5))`

Combine like terms on top.

`(-11b - 30)/(20(b - 5))`

Factor out a -1 from the top.

`(-11b - 30)/(20(b - 5)) = (-1(11b + 30))/(20(b - 5))`

Multiplying the (b - 5) by the -1 that we factored out on top.

`(11b + 30)/(20(5 - b))`

 

oldnick's profile pic

oldnick | (Level 1) Valedictorian

Posted on

`(b+10)/(4(b-5))- (4(b+5))/(5(b-5))=` `(5(b+10)-16(b+5))/(20(b-5))` `=(5b+50-16b-80)/(20(b-5))=`

`=-(11b+30)/(20(b-5))=` `(11b+30)/(20(5-b))`

 

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